Publications
56. Alves, Rafael P., Diego S. Brito, Marcelo C. Medeiros and Ruy M. Ribeiro (2023+). Forecasting Large Realized Covariance Matrices: The Benefits of Factor Models and Shrinkage. Journal of Financial Econometrics, forthcoming. PDF file.
We propose a model to forecast large realized covariance matrices of returns, applying it to the constituents of the S\&P 500 daily. To address the curse of dimensionality, we decompose the return covariance matrix using standard firm-level factors (e.g., size, value, and profitability) and use sectoral restrictions in the residual covariance matrix. This restricted model is then estimated using vector heterogeneous autoregressive (VHAR) models with the least absolute shrinkage and selection operator (LASSO). Our methodology improves forecasting precision relative to standard benchmarks and leads to better estimates of minimum variance portfolios.
Keywords: Realized covariance, factor models, shrinkage, Lasso, machine learning, forecasting, portfolio allocation, big data.
55. Fan, Jianqing, Ricardo P. Masini and Marcelo C. Medeiros (2023). Bridging Sparse and Factor Models. Annals of Statistics, 51, 1692–1717. PDF file.
Factor and sparse models are two widely used methods to impose a low-dimensional structure in high-dimension. They are seemingly mutually exclusive. We propose a lifting method that combines the merits of these two models in a supervised learning methodology that allows to efficiently explore all the information in high-dimensional datasets. The method is based on a flexible model for high-dimensional panel data, called factor-augmented regression (FarmPredict) model with both observable or latent common factors, as well as idiosyncratic components. This model not only includes both principal component (factor) regression and sparse regression as specific models but also significantly weakens the cross-sectional dependence and hence facilitates model selection and interpretability. The methodology consists of three steps. At each step, the remaining cross-section dependence can be inferred by a novel test for covariance structure in high-dimensions. We developed asymptotic theory for the FarmPredict model and demonstrated the validity of the multiplier bootstrap for testing high-dimensional covariance structure. This is further extended to testing high-dimensional partial covariance structures. The theory is supported by a simulation study and applications to the construction of a partial covariance network of the financial returns and a prediction exercise for a large panel of macroeconomic time series from FRED-MD database.
Keywords: Principal component analysis, penalized least-squares, high-dimensional inference, FarmPredict, covariance structure, partial covariance structure, LASSO.
54. Collazos, Julian, Ronaldo Dias, and Marcelo C. Medeiros (2023). Modeling the Evolution of Deaths from Infectious Diseases with Functional Data Models: The Case of COVID-19 in Brazil. Statistics in Medicine, 42, 993-1012. PDF file.
In this paper, we apply statistical methods for functional data to explore the heterogeneity in the registered number of deaths of COVID-19, over time. The cumulative daily number of deaths in regions across Brazil is treated as continuous curves (functional data). The first stage of the analysis applies clustering methods for functional data to identify and describe potential heterogeneity in the curves and their functional derivatives. The estimated clusters are labeled with different ``levels of alert'' to identify cities in a possible critical situation. In the second stage of the analysis, we apply a functional quantile regression model for the death curves to explore the associations with functional rates of vaccination and stringency and also with several scalar geographical, socioeconomic and demographic covariates. The proposed model gave a better curve fit at different levels of the cumulative number of deaths when compared to a functional regression model based on ordinary least squares. Our results add to the understanding of the development of COVID-19 death counts.
53. Caner, Mehmet, Marcelo C. Medeiros, and Gabriel Vasconcelos (2023). Sharpe Ratio Analysis in High Dimensions: Residual-Based Nodewise Regression in Factor Models. Journal of Econometrics, 235, 393-417. PDF file. Supplementary Material.
We provide a new theory for nodewise regression when the residuals from a fitted factor model are used. We apply our results to the analysis of the consistency of Sharpe Ratio estimators when there are many assets in a portfolio. We allow for an increasing number of assets as well as time observations of the portfolio. Since the nodewise regression is not feasible due to the unknown nature of idiosyncratic errors, we provide a feasible-residual-based nodewise regression to estimate the precision matrix of errors which is consistent even when number of assets, p, exceeds the time span of the portfolio, n. In another new development, we also show that the precision matrix of returns can be estimated consistently, even with an increasing number of factors and p>n. We show that: (1) with p>n, the Sharpe Ratio estimators are consistent in global minimum-variance and mean-variance portfolios; and (2) with p>n, the maximum Sharpe Ratio estimator is consistent when the portfolio weights sum to one; and (3) with p<<n, the maximum-out-of-sample Sharpe Ratio estimator is consistent.
Keywords: Sharpe Ratio; nodewise regression; high-dimensions; portfolio optimization; precision matrix.
DOI: https://doi.org/10.1016/j.jeconom.2022.03.009
52. Fan, Jianqing, Ricardo P. Masini, and Marcelo C. Medeiros (2022). Do We Exploit all Information for Counterfactual Analysis? Benefits of Factor Models and Idiosyncratic Correction. Journal of the American Statistical Association, 117, 574-590. PDF file. Supplementary Material. Data and codes.
Optimal pricing, that is determining the price level that maximizes profit or revenue of a given product, is a vital task for the retail industry. To select such a quantity, one needs first to estimate the price elasticity from the product demand. Regression methods usually fail to recover such elasticities due to confounding effects and price endogeneity. Therefore, randomized experiments are typically required. However, elasticities can be highly heterogeneous depending on the location of stores, for example. As the randomization frequently occurs at the municipal level, standard difference-in-differences methods may also fail. Possible solutions are based on methodologies to measure the effects of treatments on a single (or just a few) treated unit(s) based on counterfactuals constructed from artificial controls. For example, for each city in the treatment group, a counterfactual may be constructed from the untreated locations. In this article, we apply a novel high-dimensional statistical method to measure the effects of price changes on daily sales from a major retailer in Brazil. The proposed methodology combines principal components (factors) and sparse regressions, resulting in a method called Factor-Adjusted Regularized Method for Treatment evaluation (FarmTreat). The data consist of daily sales and prices of five different products over more than 400 municipalities. The products considered belong to the sweet and candies category and experiments have been conducted over the years of 2016 and 2017. Our results confirm the hypothesis of a high degree of heterogeneity yielding very different pricing strategies over distinct municipalities. Supplementary materials for this article are available online.
Keywords: Counterfactual; demand estimation; factor models; high-dimensional testing; optimal pricing.
DOI: https://doi.org/10.1080/01621459.2021.2004895
51. Masini, Ricardo P., Marcelo C. Medeiros and Eduardo F. Mendes (2022). Regularized Estimation of High-Dimensional Vector AutoRegressions with Weakly Dependent Innovations. Journal of Time Series Analysis, 43, 532-557. PDF file.
There has been considerable advance in understanding the properties of sparse regularization procedures in high-dimensional models. In time series context, it is mostly restricted to Gaussian autoregressions or mixing sequences. We study oracle properties of LASSO estimation of weakly sparse vector-autoregressive models with heavy tailed, weakly dependent innovations. In contrast to current literature, our innovation process satisfy an L1-mixingale type condition on the centered conditional covariance matrices. This condition covers L1-NED sequences and strong (alpha-) mixing sequences as a particular example.
Keywords: high-dimensional time series, LASSO, VAR, mixing
DOI: https://doi.org/10.1111/jtsa.12627
50. Medeiros, Marcelo C., Alexandre Street, Davi M. Valladão, Gabriel Vasconcelos and Eduardo Zilberman (2022). Short-Term Covid-19 Forecast for Latecomers. International Journal of Forecasting, 38, 467-488. PDF file.
The number of new Covid-19 cases is still high in several countries, despite vaccination efforts. A number of countries are experiencing new and severe waves of infection. Therefore, the availability of reliable forecasts for the number of cases and deaths in the coming days is of fundamental importance. We propose a simple statistical method for short-term real-time forecasting of the number of Covid-19 cases and fatalities in countries that are latecomers—i.e., countries where cases of the disease started to appear some time after others. In particular, we propose a penalized LASSO regression model with an error correction mechanism to construct a model of a latecomer country in terms of other countries that were at a similar stage of the pandemic some days before. By tracking the number of cases in those countries, we use an adaptive rolling-window scheme to forecast the number of cases and deaths in the latecomer. We apply this methodology to 45 countries and we provide detailed results for four of them: Brazil, Chile, Mexico, and Portugal. We show that the methodology performs very well when compared to alternative methods. These forecasts aim to foster better short-run management of the healthcare system and can be applied not only to countries but also to different regions within a country. Finally, the modeling framework derived in the paper can be applied to other infectious diseases.
Keywords: Covid-19, LASSO, Forecasting, Pandemics, Infectious diseases
DOI: https://doi.org/10.1016/j.ijforecast.2021.09.013
49. Johnson, James A., Marcelo C. Medeiros and Bradley S. Paye (2022). Jumps in Stock Prices: New Insights from Old Data. Journal of Financial Markets, 60, 100708. PDF file.
We characterize jump dynamics in U.S. stock market returns using a novel series of intraday prices covering almost 90 years. Jump dynamics vary substantially over time. Trends in jump activity relate to secular shifts in the nature of news. Unscheduled news often involving major wars drives jump activity in early decades, whereas scheduled news and especially news pertaining to monetary policy drives jump activity in recent decades. Jump variation measures forecast excess stock market returns, consistent with theory. Results support models featuring a separate jump factor, such that risk premium dynamics are not fully captured by volatility state variables.
Keywords: Stock market jumps, Discontinuities, Equity premium, Realized variance, Announcements, Stock return predictability
DOI: https://doi.org/10.1016/j.finmar.2022.100708
48. Bollerslev, Tim, Marcelo C. Medeiros, Andrew Patton, and Rogier Quaedvlieg (2022). From Zero to Hero: Realized Partial (Co)Variances. Journal of Econometrics, 231, 348-360. PDF file. Supplementary Material.
This paper proposes a generalization of the class of realized semivariance and semicovariance measures introduced by Barndorff-Nielsen et al. (2010) and Bollerslev et al. (2020a) to allow for a finer decomposition of realized (co)variances. The new “realized partial (co)variances” allow for multiple thresholds with various locations, rather than the single fixed threshold of zero used in semi (co)variances. We adopt methods from machine learning to choose the thresholds to maximize the out-of-sample forecast performance of time series models based on realized partial (co)variances. We find that in low dimensional settings it is hard, but not impossible, to improve upon the simple fixed threshold of zero. In large dimensions, however, the zero threshold embedded in realized semi covariances emerges as a robust choice.
Keywords: High-frequency data, Realized variation, Volatility forecasting
DOI: https://doi.org/10.1016/j.jeconom.2021.04.013
47. Masini, Ricardo P., Eduardo F. Mendes, and Marcelo C. Medeiros (2022+). Machine Learning Advances for Time Series Forecasting. Journal of Economic Surveys, forthcoming. PDF file.
In this paper, we survey the most recent advances in supervised machine learning (ML) and high-dimensional models for time-series forecasting. We consider both linear and nonlinear alternatives. Among the linear methods, we pay special attention to penalized regressions and ensemble of models. The nonlinear methods considered in the paper include shallow and deep neural networks, in their feedforward and recurrent versions, and tree-based methods, such as random forests and boosted trees. We also consider ensemble and hybrid models by combining ingredients from different alternatives. Tests for superior predictive ability are briefly reviewed. Finally, we discuss application of ML in economics and finance and provide an illustration with high-frequency financial data.
Keywords: Bagging, Boosting, Deep Learning, Forecasting, Machine Learning, Neural Networks, Nonlinear Models, Penalized Regressions, Random Forests, Regression Trees, Regularization, Sieve Approximation, Statistical Learning Theory
DOI: https://doi.org/10.1111/joes.12429
46. Masini, Ricardo P. and Marcelo C. Medeiros (2022). Counterfactual Analysis and Inference with Nonstationary Data. Journal of Business and Economic Statistics, 40, 227-239. PDF file. Supplementary Material.
Recently, there has been growing interest in developing econometric tools to conduct counterfactual analysis with aggregate data when a single “treated” unit suffers an intervention, such as a policy change, and there is no obvious control group. Usually, the proposed methods are based on the construction of an artificial/synthetic counterfactual from a pool of “untreated” peers, organized in a panel data structure. In this article, we investigate the consequences of applying such methodologies when the data comprise integrated processes of order 1, I(1), or are trend-stationary. We find that for I(1) processes without a cointegrating relationship (spurious case) the estimator of the effects of the intervention diverges, regardless of its existence. Although spurious regression is a well-known concept in time-series econometrics, they have been ignored in most of the literature on counterfactual estimation based on artificial/synthetic controls. For the case when at least one cointegration relationship exists, we have consistent estimators for the intervention effect albeit with a nonstandard distribution. Finally, we discuss a test based on resampling which can be applied when there is at least one cointegration relationship or when the data are trend-stationary.
Keywords: ArCo, Cointegration, Counterfactual Analysis, Nonstationarity, Policy Evaluation, Synthetic Control
DOI: https://doi.org/10.1080/07350015.2020.1799814
45. Masini, Ricardo P. and Marcelo C. Medeiros (2021). Counterfactual Analysis with Artificial Controls: Inference, High-Dimensions and Nonstationarity. Journal of the American Statistical Association, 116, 1773-1788. PDF file. Supplementary Material.
Recently, there has been growing interest in developing statistical tools to conduct counterfactual analysis with aggregate data when a single “treated” unit suffers an intervention, such as a policy change, and there is no obvious control group. Usually, the proposed methods are based on the construction of an artificial counterfactual from a pool of “untre ated” peers, organized in a panel data structure. In this article, we consider a general framework for counterfactual analysis for high-dimensional, nonstationary data with either deterministic and/or stochastic trends, which nests well-established methods, such as the synthetic control. We propose a resampling procedure to test intervention effects that does not rely on postintervention asymptotics and that can be used even if there is only a single observation after the intervention. A simulation study is provided as well as an empirical application. Supplementary materials for this article are available online.
Keywords: Cointegration, Comparative studies, panel data, Intervention, Policy evaluation, Resampling, Synthetic control
DOI: https://doi.org/10.1080/01621459.2021.1964978
44. Medeiros, Marcelo C., Gabriel F. Vasconcelos, Alvaro Veiga and Eduardo Zilberman (2021). Forecasting Inflation in a Data-Rich Environment: The Benefits of Machine Learning Methods. Journal of Business and Economic Statistics, 39, 98-119. PDF file. Supplementary Material.
Inflation forecasting is an important but difficult task. Here, we explore advances in machine learning (ML) methods and the availability of new datasets to forecast U.S. inflation. Despite the skepticism in the previous literature, we show that ML models with a large number of covariates are systematically more accurate than the benchmarks. The ML method that deserves more attention is the random forest model, which dominates all other models. Its good performance is due not only to its specific method of variable selection but also the potential nonlinearities between past key macroeconomic variables and inflation.
Keywords: Big Data, Inflation Forecasting, LASSO, Machine Learning, Random Forests
DOI: https://doi.org/10.1080/07350015.2019.1637745
43. Kappe, Eelco, Wayne S. DeSarbo and Marcelo C. Medeiros (2018). A Smooth Transition Finite Mixture Model for Accommodating Unobserved Heterogeneity. Journal of Business and Economic Statistics, 38, 580-592. PDF file. Supplementary Material.
While the smooth transition model has become popular in business and economics, the treatment of unobserved heterogeneity within these models has received limited attention. We propose a smooth transition finite mixture (STFM) model which simultaneously estimates the presence of time-varying effects and unobserved heterogeneity in a panel data context. Our objective is to accurately recover the heterogeneous effects of our independent variables of interest while simultaneously allowing these effects to vary over time. Accomplishing this objective may provide valuable insights for managers and policy makers. The STFM model nests several well-known smooth transition and threshold models. We develop the specification, estimation, and model selection criteria for the STFM model using Bayesian methods. We also provide a theoretical assessment of the flexibility of the STFM model when the number of regimes grows with the sample size. In an extensive simulation study, we show that ignoring unobserved heterogeneity can lead to distorted parameter estimates, and that the STFM model is fairly robust when underlying model assumptions are violated. Empirically, we estimate the effects of in-game promotions on game attendance in Major League Baseball. Empirical results show that the STFM model outperforms all its nested versions.
Keywords: Latent Class, Major League Baseball, Markov Chain Monte Carlo, Model Selection, Regime-Switching
DOI: https://doi.org/10.1080/07350015.2018.1543126
42. Carvalho, Carlos V., Ricardo P. Masini and Marcelo C. Medeiros (2018). ArCo: An Artificial Counterfactual Approach for High-Dimensional Panel Time-Series Data. Journal of Econometrics, 207, 353-380. PDF file. Supplementary Material.
We consider a new, flexible and easy-to-implement method to estimate the causal effects of an intervention on a single treated unit when a control group is not available and which nests previous proposals in the literature. It is a two-step methodology where in the first stage, a counterfactual is estimated based on a large-dimensional set of variables from a pool of untreated units by means of shrinkage methods, such as the \emph{least absolute shrinkage and selection operator} (LASSO). In the second stage, we estimate the average intervention effect on a vector of variables, which is consistent and asymptotically normal. Our results are valid uniformly over a wide class of probability laws. We show that these results hold even when the exact date of the intervention is unknown. Tests for multiple interventions and for contamination effects are derived. By a simple transformation of the variables, it is possible to test for multivariate intervention effects on several moments of the variables of interest. Existing methods in the literature usually test for intervention effects on a single variable and assume that the time of the intervention is known. In addition, high-dimensionality is frequently ignored and inference is either conducted under a set of more stringent hypotheses and/or by permutation tests. A Monte Carlo experiment evaluates the properties of the method in finite samples and compares it with other alternatives. As an application, we evaluate the effects on inflation, GDP growth, retail sales and credit of an anti tax-evasion program.
Keywords: counterfactual analysis, comparative studies, treatment effects, synthetic control, policy evaluation, LASSO, structural break, factor models.
DOI: https://doi.org/10.1016/j.jeconom.2018.07.005
41. Fonseca, Yuri R., Ricardo P. Masini, Marcelo C. Medeiros and Gabriel F. R. Vasconcelos (2018). ArCo: An R package to Estimate Artificial Counterfactuals. The R Journal, 10, 91-108. PDF file.
In this paper we introduce the ArCopackage for R which consists of a set of functionsto implement the the Artificial Counterfactual (ArCo) methodology to estimate causal effects of anintervention (treatment) on aggregated data and when a control group is not necessarily available.The ArCo method is a two-step procedure, where in the first stage a counterfactual is estimated from alarge panel of time series from a pool of untreated peers. In the second-stage, the average treatmenteffect over the post-intervention sample is computed. Standard inferential procedures are available.The package is illustrated with both simulated and real datasets.
Keywords: ArCo, R package, counterfactuals, synthetic control.
40. Garcia, Márcio, Marcelo C. Medeiros and Gabriel Vasconcelos (2017). Real-Time Inflation Forecasting with High-Dimensional Models: The Case of Brazil. International Journal of Forecasting, 33, 679-693. PDF file.
We show that high-dimensional econometric models, such as shrinkage and complete subset regression, perform very well in real time forecasting of inflation in data-rich environments. We use Brazilian inflation as an application. It is an ideal example because it exhibits high short-term volatility and several agents devote extensive resources to forecast its short-term behavior. Therefore, precise specialist's forecasts are available both as a benchmark and as an important candidate regressor for the forecasting models. Furthermore, we combine forecasts based on model confidence sets and we show that model combination can achieve superior predictive performance.
Keywords: real-time inflation forecasting, emerging markets, shrinkage, factor models, LASSO, regression trees, random forests, complete subset regression, machine learning, model confidence set, forecast combination, expert forecasts.
DOI: http://10.0.3.248/j.ijforecast.2017.02.002
39. Medeiros, Marcelo C. and Eduardo F. Mendes (2017). Adaptive Lasso estimation for ARDL models with GARCH innovations. Econometric Reviews, 36, 622-637. PDF file.
In this paper we show the validity of the adaptive LASSO procedure in estimating stationary ARDL(p,q) models with innovations in a broad class of conditionally heteroskedastic models. We show that the adaptive Lasso selects the relevant variables with probability converging to one and that the estimator is oracle efficient, meaning that its distribution converges to the same distribution of the oracle assisted least squares, i.e., the least squares estimator calculated as if we knew the set of relevant variables beforehand. Finally, we show that the LASSO estimator can be used to construct the initial weights. The performance of the method in finite samples is illustrated using Monte Carlo simulation.
Keywords: ARDL, GARCH, sparse models, shrinkage, LASSO, adaLASSO, time series.
DOI: 10.1080/07474938.2017.1307319
38. Callot, Laurent, Anders B. Kock and Marcelo C. Medeiros (2017). Modeling and Forecasting Large Realized Covariance Matrices and Portfolio Choice. Journal of Applied Econometrics, 32, 140-158. PDF file. Supplementary Material.
We consider modelling and forecasting of large realized covariance matrices by penalized vector autoregressive models. We consider Lasso-type estimators to reduce the dimensionality to a manageable one and provide strong theoretical guarantees on the forecast capability of our procedure. We show that we can forecast realized covariance matrices almost as precisely as if we had known the true driving dynamics of these in advance. We next investigate the sources of these driving dynamics for the realized covariance matrices of the 30 Dow Jones stocks and find that these dynamics are not stable as the data are aggregated from the daily to the weekly and monthly frequencies. The theoretical guarantees on our forecasts are illustrated on the Dow Jones index. In particular, we can beat our benchmark by a wide margin at the longer forecast horizons. Finally, we investigate the economic value of our forecasts in a portfolio selection exercise and find that in certain cases an investor is willing to pay a considerable amount in order get access to our forecasts.
Keywords: Realized covariance, shrinkage, Lasso, forecasting, portfolio allocation.
DOI: http://dx.doi.org/10.1002/jae.2512
37. Berriel, Tiago C., Marcelo C. Medeiros and Marcelo Sena (2016). Instrument selection for estimation of a forward-looking Phillips Curve. Economics Letters, PDF file, 145, 123-125.
We show that data-driven instrument selection based on the LASSO estimator can perform well comparative to the usual ad hoc instrument set for single equation estimation of a forward-looking Phillips Curve. We conclude that in face of model uncertainty and/or potentially weak instruments within a large number of candidates, data-driven selection may provide a disciplined and more reliable estimation strategy.
Keywords: instruments, model selection, shrinkage.
DOI: http://dx.doi.org/10.1016/j.econlet.2016.05.032
36. Medeiros, Marcelo C. and Gabriel Vasconcelos (2016). Forecasting Macroeconomic Variables in Data-Rich Environments. Economics Letters, 138, 50-52. PDF file.
We show that high-dimensional models produce, on average, smaller forecasting errors for macroeconomic variables when we consider a large set of predictors. Our results showed that a good selection of the adaptive LASSO hyperparameters also reduces forecast errors.
Keywords: big data, forecasting, LASSO, shrinkage, model selection.
DOI: 10.1016/j.econlet.2015.11.017
35. Medeiros, Marcelo C. and Eduardo F. Mendes (2016). l1-Regularization of High-dimensional Time-Series Models with Non-Gaussian and Heteroskedastic Innovations. (This is an updated and major revised version of the manuscript "Estimating High-Dimensional Time Series Models" and " l1-Regularization of High-dimensional Time-Series Models with Flexible Innovations"). Journal of Econometrics, 191, 255-271. PDF file.
We study the asymptotic properties of the Adaptive LASSO (adaLASSO) in sparse, high-dimensional, linear time-series models. We assume that both the number of covariates in the model and the number of candidate variables can increase with the sample size (polynomially or geometrically). In other words, we let the number of candidate variables to be larger than the number of observations. We show the adaLASSO consistently chooses the relevant variables as the number of observations increases (model selection consistency) and has the oracle property, even when the errors are non-Gaussian and conditionally heteroskedastic. This allows the adaLASSO to be applied to a myriad of applications in empirical finance and macroeconomics. A simulation study shows that the method performs well in very general settings with $t$-distributed and heteroskedastic errors as well with highly correlated regressors. Finally, we consider an application to forecast monthly US inflation with many predictors. The model estimated by the adaLASSO delivers superior forecasts than traditional benchmark competitors such as autoregressive and factor models.
Keywords: sparse models, shrinkage, LASSO, adaLASSO, time series, forecasting.
DOI: 10.1016/j.jeconom.2015.10.011
34. Hillebrand, Eric and Marcelo C. Medeiros (2016). Asymmetries, Breaks, and Long-Range Dependence. Journal of Business and Economic Statistics, 34, 23-41. PDF file.
We study the simultaneous occurrence of long memory and nonlinear effects, such as parameter changes and threshold effects, in time series models and apply our modeling framework to daily realized measures of integrated variance. Asymptotic theory for parameter estimation is developed and two model building procedures are proposed. The methodology is applied to stocks of the Dow Jones Industrial Average during the period 2000 to 2009. We find strong evidence of nonlinear effects in financial volatility. An out-of-sample analysis shows that modeling these effects can improve forecast performance.
Keywords: Smooth transitions, long memory, forecasting, realized variance.
DOI: 10.1080/07350015.2014.985828
33. Fernandes, Marcelo, Marcelo C. Medeiros, and Alvaro Veiga (2016). A (semi-)parametric functional coefficient autoregressive conditional duration model. Econometric Reviews, 35, 1221-1250. PDF file
In this paper, we propose a class of logarithmic ACD-type models that accommodates overdispersion, intermittent dynamics, multiple regimes, and asymmetries in financial durations. In particular, our functional coefficient logarithmic autoregressive conditional duration (FC-LACD) model relies on a smooth-transition autoregressive specification. The motivation lies on the fact that the latter yields a universal approximation if one lets the number of regimes grows without bound. After establishing sufficient conditions for strict stationarity, we address model identifiability as well as the asymptotic properties of the quasi-maximum likelihood (QML) estimator for the FC-LACD model with a fixed number of regimes. In addition, we also discuss how to consistently estimate a semiparametric variant of the FC-LACD model that takes the number of regimes to infinity. An empirical illustration indicates that our functional coefficient model is flexible enough to model IBM price durations.
Keywords: explosive regimes, neural networks, quasi-maximum likelihood, sieve estimation, smooth transition, stationarity.
DOI: 10.1080/07474938.2014.977071
32. Fernandes, Marcelo, Marcelo C. Medeiros and Marcel Scharth (2014). Modeling and Predicting the CBOE Market Volatility Index. Journal of Banking and Finance, 40, 1-10. PDF file.
This paper performs a thorough statistical examination of the time-series properties of the daily market volatility index (VIX) from the Chicago Board Options Exchange (CBOE). The motivation lies on the widespread consensus that the VIX is a barometer to the overall market sentiment as to what concerns investors’ risk appetite. Our preliminary analysis suggests that the VIX index displays long-range dependence. This is well line with the strong empirical evidence in the literature supporting long memory in both options-implied and realized variances. We thus resort to both parametric and semiparametric heterogeneous autoregressive (HAR) processes for modeling and forecasting purposes. Our main findings are as follows. First, we confirm the evidence in the literature that there is a strong negative relationship between the VIX index and the S&P 500 index return as well as a positive contemporaneous link with the volume of the S&P 500 index. Second, we find that the VIX index tends to decline as the long-run oil price increases. This is not entirely surprising given the high demand from oil in the last years as well as the recent trend of shorting energy prices in the hedge fund industry. Third, the term spread has no long-run impact in the VIX index despite of the positive contemporaneous link. Fourth, there is some weak evidence that increases in the value of the US dollar tend to move down options-implied market volatility. Finally, we cannot reject the linearity of the above relationships, neither in sample nor out of sample. As for the latter, we actually show that it is pretty hard to beat the pure HAR process because of the very persistent nature of the VIX index. It is not impossible, though. We set out a semiparametric HAR-type model that performs very well across different forecasting horizons by using the above explanatory variables in a quite efficient manner.
Keywords: heterogeneous autoregression, implied volatility, neural networks, VIX.
DOI: 10.1016/j.jbankfin.2013.11.004
31. Medeiros, Marcelo C., Eduardo Mendes, and Les Oxley (2014). A Note on Nonlinear Cointegration, Misspecification and Bimodality. Econometric Reviews, 33, 713-731. PDF file
We derive the asymptotic distribution of the ordinary least squares estimator in a cointegrating regression under misspecification and/or nonlinearity in the variables. We show that, under some circumstances, the order of convergence of the estimator changes and the asymptotic distribution is non-standard. The t-statistic might also diverge. A simple case arises when the intercept is erroneously omitted from the estimated model or in nonlinear-in-variables models with endogenous regressors. In the latter case, a solution is to use an instrumental variable estimator. The core results in this paper also generalise to more complicated nonlinear models involving integrated time series.
Keywords: Cointegration, nonlinearity, bimodality, misspecification, asymptotic theory.
DOI: 10.1080/07474938.2012.690676
30. Hillebrand, Eric, Marcelo C. Medeiros, and Junyue Xu (2013). Asymptotic Theory for Regressions with Smoothly Changing Parameters. Journal of Time Series Econometrics, 5, 133-162. PDF file
We derive the asymptotic properties of the quasi maximum likelihood estimator of smooth transition regressions when time is the transition variable. The consistency of the estimator and its asymptotic distribution are examined. It is shown that the estimator converges at the usual rate and has an asymptotically normal distribution. The finite sample properties of the estimator are explored in simulations.
Keywords: Regime switching, smooth transition regression, asymptotic theory.
29. Asai, Manabu, Michael McAleer, and Marcelo C. Medeiros (2012). Asymmetry and Long Memory in Volatility Modelling. Journal of Financial Econometrics, 10, 495-512. PDF file
In this paper, we propose a long memory asymmetric volatility model which captures more flexible asymmetric patterns as compared with several existing models. We extend the new specification to realized volatility by taking account of measurement errors, and use the Efficient Importance Sampling technique to estimate the model. We apply the model to the realized volatility of S&P500. Overall, the results of the out-of-sample forecasts show the adequacy of the new asymmetric and long memory volatility model for the period including the global financial crisis.
Keywords: Asymmetric volatility, long memory, realized volatility, measurement errors, efficient importance sampling.
28. Asai, Manabu, Michael McAleer, and Marcelo C. Medeiros (2012). Modelling and Forecasting Noisy Realized Volatility. Computational Statistics and Data Analysis, 56, 217-230. PDF file
Several methods have recently been proposed in the ultra-high frequency financial literature to remove the effects of microstructure noise and to obtain consistent estimates of the integrated volatility (IV) as a measure of ex post daily volatility. Even bias-corrected and consistent realized volatility (RV) estimates of IV can contain residual microstructure noise and other measurement errors. Such noise is called ‘‘realized volatility error’’. As such errors are ignored, we need to take account of them in estimating and forecasting IV. This paper investigates through Monte Carlo simulations the effects of RV errors on estimating and forecasting IV with RV data. It is found that: (i) neglecting RV errors can lead to serious bias in estimators; (ii) the effects of RV errors on one-step-ahead forecasts are minor when consistent estimators are used and when the number of intraday observations is large; (iii) even the partially corrected R2 recently proposed in the literature should be fully corrected for evaluating forecasts. This paper proposes a full correction of R2. An empirical example for S&P 500 data is used to demonstrate the techniques developed in this paper.
Keywords: realized volatility; diffusion; financial econometrics; measurement errors; forecasting; model evaluation; goodness-of-fit.
DOI: 10.1016/j.csda.2011.06.024
27. Preve, Daniel and Marcelo C. Medeiros. Linear Programming-Based Estimators in Simple Linear Regression (2011). Journal of Econometrics, 165, 128-136. PDF file
In this paper we introduce a linear programming estimator (LPE) for the slope parameter in a constrained linear regression model with a single regressor. The LPE is interesting because it can be superconsistent in the presence of an endogenous regressor and, hence, preferable to the ordinary least squares estimator (LSE). Two different cases are considered as we investigate the statistical properties of the LPE. In the first case, the regressor is assumed to be fixed in repeated samples. In the second, the regressor is stochastic and potentially endogenous. For both cases the strong consistency and exact finite-sample distribution of the LPE is established. Conditions under which the LPE is consistent in the presence of serially correlated, heteroskedastic errors are also given. Finally, we describe how the LPE can be extended to the case with multiple regressors and conjecture that the extended estimator is consistent under conditions analogous to the ones given herein. Finite-sample properties of the LPE and extended LPE in comparison to the LSE and instrumental variable estimator (IVE) are investigated in a simulation study. One advantage of the LPE is that it does not require an instrument.
Keywords: Linear programming estimators, instrumental variables, linear regression, asymptotic theory.
DOI: 10.1016/j.jeconom.2011.05.011
26. Areosa, Waldyr, Michael McAleer and Marcelo C. Medeiros (2011). Moment Based Estimation of Smooth Transition Regression Models with Endogenous Variables. Journal of Econometrics, 165, 100-111. PDF file
Nonlinear regression models have been widely used in practice for a variety of time series and cross-section datasets. For purposes of analyzing univariate and multivariate time series data, in particular, the Smooth Transition Regression (STR) models have been shown to be very useful for representing and capturing asymmetric behavior. Most STR models have been applied to univariate process, and have assumed a variety of assumptions, including stationary or cointegrated processes, uncorrelated and homoskedastic or conditionally heteroskedastic errors, and weakly exogenous regressors. Under the assumption of exogeneity, the standard method of estimation is nonlinear least squares. The primary purpose of this paper is to relax the assumption of weakly exogenous regressors and to discuss instrumental variable methods for estimating STR models. The paper analyzes the properties of the STR model with endogenous variables by providing a diagnostic test of linearity of the underlying process under endogeneity, developing an estimation procedure for the STR model, presenting the results of Monte Carlo simulations to show the usefulness of the model and estimation method, and providing an empirical application for inflation rate targeting in Brazil. We show that STR models with endogenous variables can be specified and estimated by straightforward application of current results in the literature.
Keywords: Smooth transition regressions, switching regressions, generalized method of moments, Phillips curve.
DOI: 10.1016/j.jeconom.2011.05.009
25. Audrino, Francesco and Marcelo C. Medeiros (2011). Modeling and Forecasting Short-term Interest Rates: The Benefits of Smooth Regimes, Macroeconomic Variables, and Bagging. Journal of Applied Econometrics, 26, 999-1022. PDF file
In this paper we propose a smooth transition tree model for both the conditional mean and variance of the short-term interest rate process. The estimation of such models is addressed and the asymptotic properties of the quasi-maximum likelihood estimator are derived. Model specification is also discussed. When the model is applied to the US short-term interest rate we find (1) leading indicators for inflation and real activity are the most relevant predictors in characterizing the multiple regimes’ structure; (2) the optimal model has three limiting regimes. Moreover, we provide empirical evidence of the power of the model in forecasting the first two conditional moments when it is used in connection with bootstrap aggregation (bagging).
Keywords: Regression trees, smooth transition models, forecasting interest rates, bagging.
DOI: 10.1002/jae.1171
24. McAleer, Michael and Marcelo C. Medeiros (2011). Forecasting Realized Volatility with Linear and Nonlinear Models. Journal of Economic Surveys, 25, 6-18. PDF file.
In this paper we consider a nonlinear model based on neural networks as well as linear models to forecast the daily volatility of the S&P 500 and FTSE 100 indexes. As a proxy for daily volatility, we consider a consistent and unbiased estimator of the integrated volatility that is computed from high frequency intra-day returns. We also consider a simple algorithm based on bagging (bootstrap aggregation) in order to specify the models analyzed in this paper.
Keywords: Realized volatility, forecasting, nonlinear models, bagging.
DOI: 10.1002/jae.1171
23. Aznarte, José Luis, Marcelo C. Medeiros, and José Manuel Benítez Sánchez (2010). Testing for Remaining Autocorrelation of the Residuals in the Framework of Fuzzy Rule-based Time Series Modelling. International Journal of Uncertainty, Fuzziness and Knowledge-based Systems, 18, 371-387. PDF file
In this paper, we propose a new diagnostic checking tool for fuzzy rule-based modelling of time series. Through the study of the residuals in the LagrangeMultiplier testing framework we devise a hypothesis test which allows us to determine if there is some left autocorrelation in the error series. This is an important step towards a statistically sound modelling strategy for fuzzy rule-based models.
Keywords: Statistical test, fuzzy rule based models, residual analysis, autocorrelation.
DOI: 10.1142/S021848851000660X
22. Aznarte, José Luis, Marcelo C. Medeiros, and José Manuel Benítez Sánchez (2010). Linearity Testing Against a Fuzzy Rule-based Model. Fuzzy Sets and Systems, 161, 1836-1851. PDF file.
In this paper, we introduce a linearity test for fuzzy rule-based models in the framework of time series modeling. To do so, we explore a family of statistical models, the regime switching autoregressive models, and the relations that link them to the fuzzy rule-based models. From these relations, we derive a Lagrange Multiplier linearity test and some properties of the maximum likelihood estimator needed for it. Finally, an empirical study of the goodness of the test is presented.
Keywords: Fuzzy models, linearity testing, time series.
DOI: 10.1016/j.fss.2010.01.005
21. Hillebrand, Eric and Marcelo C. Medeiros (2010). The Benefits of Bagging for Forecast Models of Realized Volatility. Econometric Reviews, 29, 571-593. PDF file.
This paper shows that bagging can improve the forecast accuracy of time series models for realized volatility. We consider 23 stocks from the Dow Jones Industrial Average over the sample period 1995 to 2005 and employ two different forecast models, a log-linear specification in the spirit of the heterogeneous autoregressive model and a nonlinear specification with logistic transitions. Both forecast model types benefit from bagging, in particular in the 1990s part of our sample. The log-linear specification shows larger improvements than the nonlinear model. Bagging the log-linear model yields the highest forecast accuracy on our sample.
Keywords: Realized volatility, forecasting, nonlinear models, neural networks, bagging.
DOI:10.1080/07474938.2010.481554
20. Scharth, Marcel and Marcelo C. Medeiros (2009). Asymmetric Effects and Long Memory in the Volatility of Dow Jones Stocks. International Journal of Forecasting, 25, 304-327. PDF file
Does volatility reflect a continuous reaction to past shocks or do changes in the markets induce shifts in the volatility dynamics? In this paper, we provide empirical evidence that cumulated price variations convey meaningful information about multiple regimes in the realized volatility of stocks, where large falls (rises) in prices are linked to persistent regimes of high (low) variance in stock returns. Incorporating past cumulated daily returns as an explanatory variable in a flexible and systematic nonlinear framework, we estimate that falls of different magnitudes over less than two months are associated with volatility levels 20\% and 60\% higher than the average of periods with stable or rising prices. We show that this effect accounts for large empirical values of long memory parameter estimates. Finally, we show that while introducing more realistic dynamics for volatility, the model is able to at least retain or improve overall out of sample performance in forecasting when compared to standard methods. Most importantly, the model is more robust to periods of financial crises, when it attains significantly better forecasts.
Keywords: Realized volatility, regression trees, smooth transition, forecasting.
DOI: 10.1016/j.ijforecast.2009.01.008
19. Medeiros, Marcelo C. and Álvaro Veiga (2009). Modeling Multiple Regimes in Financial Volatility with a Flexible Coefficient GARCH Model. Econometric Theory, 25, 117-161. PDF file
In this paper a flexible multiple regime GARCH(1,1)-type model is developed to describe the sign and size asymmetries and intermittent dynamics in financial volatility. The results of the paper are important to other nonlinear GARCH models. The proposed model nests some of the previous specifications found in the literature and has the following advantages: First, contrary to most of the previous models, more than two limiting regimes are possible and the number of regimes is determined by a simple sequence of of tests that circumvents identification problems that are usually found in nonlinear time series models. The second advantage is that the stationarity restriction on the parameters is relatively weak, thereby allowing for rich dynamics. It is shown that the model may have explosive regimes but can still be strictly stationary and ergodic. A simulation experiment shows that the proposed model can generate series with high kurtosis, low first-order autocorrelation of the squared observations, and exhibit the so-called "Taylor effect"', even with Gaussian errors. Estimation of the parameters is addressed and the asymptotic properties of the quasi-maximum likelihood estimator are derived under weak conditions. A Monte-Carlo experiment is designed to evaluate the finite sample properties of the sequence of tests. Empirical examples are also considered.
Keywords: GARCH models, multiple regimes, smooth transition, volatility, asymmetry.
18. Medeiros, Marcelo C., Michael McAleer, Daniel Slottje, Vicente Ramos and Javier Rey-Maquieira (2008). An Alternative Approach to Estimating Demand: Neural Network Regression with Conditional Volatility for High Frequency Air Passenger Arrivals. Journal of Econometrics, 147, 372-383. PDF file
In this paper we provide an alternative approach to analyze the demand for international tourism in the Balearic Islands, Spain, by using a neural network model that incorporates time-varying conditional volatility. We consider daily air passenger arrivals to Palma de Mallorca, Ibiza and Mahon, which are located in the islands of Mallorca, Ibiza and Menorca, respectively, as a proxy for international tourism demand for the Balearic Islands. Spain is a world leader in terms of total international tourist arrivals and receipts, and Mallorca is one of the most popular destinations in Spain. For tourism management and marketing, it is essential to forecast high frequency international tourist demand accurately. As it is important to provide sensible international tourism demand forecast intervals, it is also necessary to model their variances accurately. Moreover, time-varying variances provide useful information regarding the risks associated with variations in international tourist arrivals.
Keywords: Tourist arrivals, forecasting, neural networks, GARCH models, asymptotic theory.
DOI:10.1016/j.jeconom.2008.09.018
17. McAleer, Michael, Marcelo C. Medeiros, Daniel Slottje (2008). A Neural Network Demand System with Heteroskedastic Errors. Journal of Econometrics, 104, 359-371. PDF file
In this paper we consider estimation of demand systems with flexible functional forms, allowing an error term with a general conditional heteroskedasticity function that depends on observed covariates, such as demographic variables. We propose a general model that can be either estimated by quasi-maximum likelihood (in the case of exogenous regressors) or generalized method of moments (GMM) if the covariates are endogenous. The specification proposed in the paper nests several demand functions proposed in the literature and the results in the paper can be applied to the recently proposed Exact Affine Stone Index (EASI) demand system. Furthermore, flexible nonlinear Engel curves can be estimated.
Keywords: Demand systems, neural networks, EASI demand system, Engel curves.
DOI: 10.1016/j.jeconom.2008.09.031
16. McAleer, Michael and Marcelo C. Medeiros (2008). A Multiple Regime Smooth Transition Heterogeneous Autoregressive Model for Long Memory and Asymmetries. Journal of Econometrics,147, 104-119. PDF file
In this paper we propose a flexible model to capture nonlinearities and long-range dependence in time series dynamics. The new model is a multiple regime smooth transition extension of the Heterogenous Autoregressive (HAR) model, which is specifically designed to model the behaviour of the volatility inherent in financial time series. The model is able to describe simultaneously long memory, as well as sign and size asymmetries. A sequence of tests is developed to determine the number of regimes, and an estimation and testing procedure is presented. Monte Carlo simulations evaluate the finite-sample properties of the proposed tests and estimation procedures. We apply the model to several Dow Jones Industrial Average index stocks using transaction level data from the Trades and Quotes database that covers ten years of data. We find strong support for long memory and both sign and size asymmetries. Furthermore, the new model, when combined with the linear HAR model, is viable and flexible for purposes of forecasting volatility.
Keywords: Realized volatility, approximate long memory models, smooth transitions, forecasting, nonlinear models, asymptotic theory.
DOI: 10.1016/j.jeconom.2008.09.032
15. Soares, Lacir and Marcelo C. Medeiros (2008). Modeling and Forecasting Short-Term Electricity Load: A Comparison of Methods with an Application to Brazilian Data. International Journal of Forecasting, 24, 630-644. PDF file
The goal of this paper is to describe a forecasting model for the hourly electricity load in the area covered by an electric utility located in the southeast of Brazil. A different model is constructed for each hour of the day. Each model is based on a decomposition of the daily series of each hour in two components. The first component is purely deterministic and is related to trends, seasonality, and special days effect. The second one is stochastic and follows a linear autoregressive model. Nonlinear alternatives are also considered in the second step. The multi-step forecasting performance of the proposed methodology is compared with a benchmark model and the results indicate that our proposal is useful for electricity load forecasting in tropical environments.
Keywords: Electricity load forecasting, linear and nonlinear models.
DOI: 10.1016/j.ijforecast.2008.08.003
14. Joel C. da Rosa, Alvaro Veiga, and Marcelo C. Medeiros (2008). Tree-Structured Smooth Transition Regression Models. Computational Statistics and Data Analysis, 52, 2469-2488. PDF file
This paper introduces a tree-based model that combines aspects of CART (Classification and Regression Trees) and STR (Smooth Transition Regression). The model is called the Smooth Transition Regression Tree (STR-Tree). The main idea relies on specifying a parametric nonlinear model through a tree-growing procedure. The resulting model can be analyzed as a smooth transition regression with multiple regimes. Decisions about splits are entirely based on a sequence of Lagrange Multiplier (LM) tests of hypotheses. An alternative specification strategy based on a 10-fold cross-validation is also discussed and a Monte Carlo experiment is carried out to evaluate the performance of the proposed methodology in comparison with standard techniques. The STR-Tree model outperforms CART when the correct selection of the architecture of simulated trees is discussed. Furthermore, the LM test seems to be a promising alternative to 10-fold cross-validation. Function approximation is also analyzed. When put into proof with real and simulated datasets, the STR-Tree model has a superior predictive ability than CART.
Keywords: Regression trees, smooth transitions, model building, CART.
DOI: 10.1016/j.csda.2007.08.018
13. McAleer, Michael and Marcelo C. Medeiros (2008). Realized Volatility: A Review. Econometric Reviews, 27, 10-45. PDF file.
This paper reviews the exciting and rapidly expanding literature on realized volatility. After presenting a general univariate framework for estimating realized volatilities, a simple discrete time model is presented in order to motivate the main results. A continuous time specification provides the theoretical foundation for the main results in this literature. Cases with and without microstructure noise are considered, and it is shown how microstructure noise can cause severe problems in terms of consistent estimation of the daily realized volatility. Independent and dependent noise processes are examined. The most important methods for providing consistent estimators are presented, and a critical exposition of different techniques is given. The finite sample properties are discussed in comparison with their asymptotic properties. A multivariate model is presented to discuss estimation of the realized covariances. Various issues relating to modelling and forecasting realized volatilities are considered. The main empirical findings using univariate and multivariate methods are summarized.
Keywords: Realized volatility, micro-structure noise, realized covariance.
DOI: 10.1080/07474930701853509
12. Medeiros, Marcelo C., Timo Teräsvirta and Gianluigi Rech (2006). Building Neural Network Models for Time Series: A Statistical Approach. Journal of Forecasting, 25, 49-75. PDF file
This paper is concerned with modelling time series by single hidden layer feedforward neural network models. A coherent modelling strategy based on statistical inference is presented. Variable selection is carried out using simple existing techniques. The problem of selecting the number of hidden units is solved by sequentially applying Lagrange multiplier type tests, with the aim of avoiding the estimation of unidentified models. Misspecification tests are derived for evaluating an estimated neural network model. All the tests are entirely based on auxiliary regressions and are easily implemented. A small-sample simulation experiment is carried out to show how the proposed modelling strategy works and how the misspecification tests behave in small samples. Two applications to real time series, one univariate and the other multivariate, are considered as well. Sets of one-step-ahead forecasts are constructed and forecast accuracy is compared with that of other nonlinear models applied to the same series.
Keywords: Neural networks, model building, forecasting.
DOI: 10.1002/for.974
11. Teräsvirta, Timo, Dick van Dijk and Marcelo C. Medeiros (2005). Linear Models, Smooth Transition Autoregressions and Neural Networks for Forecasting Macroeconomic Time Series: A Reexamination (with discussion). International Journal of Forecasting, 21, 755-774. PDF file
In this paper we examine the forecast accuracy of linear autoregressive, smooth transition autoregressive (STAR), and neural network (NN) time series models for 47 monthly macroeconomic variables of the G7 economies. Unlike previous studies that typically consider multiple but fixed model specifications, we use a single but dynamic specification for each model class. The point forecast results indicate that the STAR model generally outperforms linear autoregressive models. It also improves upon several fixed STAR models, demonstrating that careful specification of nonlinear time series models is of crucial importance. The results for neural network models are mixed in the sense that at long forecast horizons, an NN model obtained using Bayesian regularization produces more accurate forecasts than a corresponding model specified using the specific-to-general approach. Reasons for this outcome are discussed.
Keywords: Nonlinear models, smooth transition, neural networks, forecasting, model comparison.
DOI: 10.1016/j.ijforecast.2005.04.010
10. Medeiros, Marcelo C. and Álvaro Veiga (2005). A Flexible Coefficient Smooth Transition Time Series Model. IEEE Transactions on Neural Networks, 16, 97 - 113. PDF file
In this paper we consider a flexible smooth transition autoregressive (STAR) model with multiple regimes and multiple transition variables. This formulation can be interpreted as a time varying linear model where the coefficients are the outputs of a single hidden layer feedforward neural network. This proposal has the major advantage of nesting several nonlinear models, such as, the Self-Exciting Threshold AutoRegressive (SETAR), the AutoRegressive Neural Network (AR-NN), and the Logistic STAR models. Furthermore, if the neural network is interpreted as a nonparametric universal approximation to any Borel-measurable function, our formulation is directly comparable to the Functional Coefficient AutoRegressive (FAR) and the Single-Index Coefficient Regression models. A model building procedure is developed based on statistical inference arguments.A Monte-Carlo experiment showed that the procedure works in small samples, and its performance improves, as it should, in medium size samples. Several real examples are also addressed.
Keywords: Nonlinear models, smooth transition, neural networks, multiple regimes, model building, asymptotic theory.
9. Suarez-Fariñas, Mayte, Carlos E. Pedreira and Marcelo C. Medeiros (2004). Local-Global Neural Networks: A New Approach for Nonlinear Time Series Modelling. Journal of the American Statistical Association, 99, 1092 - 1107. PDF file
In this paper, the Local Global Neural Networks model is proposed within the context of time series models. This formulation encompasses some already existing nonlinear models and also admits the Mixture of Experts approach. We place emphasis on the linear expert case and extensively discuss the theoretical aspects of the model: stationarity conditions, existence, consistency and asymptotic normality of the parameter estimates, and model identifiability. The proposed model consists of a mixture of stationary or non-stationary linear models and is able to describe "intermittent'' dynamics: the system spends a large fraction of the time in a bounded region, but, sporadically, it develops an instability that grows exponentially for some time and then suddenly collapses. Intermittency is a commonly observed behavior in ecology and epidemiology, fluid dynamics and other natural systems. A model building strategy is also considered and the parameters are estimated by concentrated maximum likelihood. The whole procedure is illustrated with two real time-series.
Keywords: Nonlinear models, smooth transition, mixture of models, multiple-regime, asymptotic theory.
DOI: 10.1198/016214504000001691
8. Medeiros, Marcelo C., and Álvaro Veiga (2003). Diagnostic Checking in a Flexible Nonlinear Time Series Model. Journal of Time Series Analysis, 24, 461-482. PDF file
This paper considers a sequence of misspecification tests for a flexible nonlinear time series model. The model is a generalization of both the Smooth Transition AutoRegressive (STAR) and the AutoRegressive Artificial Neural Network (AR-ANN) models. The tests are Lagrange multiplier (LM) type tests of parameter constancy against the alternative of smoothly changing ones, of serial independence, and of constant variance of the error term against the hypothesis that the variance changes smoothly between regimes. The small sample behaviour of the proposed tests is evaluated by a Monte-Carlo study and the results show that the tests have size close to the nominal one and a good power.
Keywords: Nonlinear models, smooth transitions, model evaluation.
7. Medeiros, Marcelo C., Álvaro Veiga and Maurício G. C. Resende (2002). A Combinatorial Approach to Piecewise Linear Time Series Estimation. Journal of Computational and Graphical Statistics, 11, 236-258. (PDF version)
Over recent years, several nonlinear time series models have been proposed in the literature. One model that has found a large number of successful applications is the threshold autoregressive model (TAR). The TAR model is a piecewise linear process whose central idea is to change the parameters of a linear autoregressive model according to the value of an observable variable, called the threshold variable. If this variable is a lagged value of the time series, the model is called a self-exciting threshold autoregressive (SETAR) model. In this paper, we propose a heuristic to estimate a more general SETAR model, where the thresholds are multivariate. We formulate the task of finding multivariate thresholds as a combinatorial optimization problem. We develop an algorithm based on a Greedy Randomized Adaptive Search Procedure (GRASP) to solve the problem. GRASP is an iterative randomized sampling technique that has been shown to quickly produce good quality solutions for a wide variety of optimization problems. The proposed model performs well on both simulated and real data.
Keywords: Piecewise-linear models, SETAR models, nonlinearity, GRASP, combinatorial optimization.
DOI: 10.1198/106186002317375712
6. Medeiros, Marcelo C. and Timo Teräsvirta (2001). Statistical Methods for Modelling Neural Networks. Engineering Intelligent Systems, 9, 227-235. PDF file
In this paper modelling time series by single hidden layer feedforward neural network models is considered. A coherent modelling strategy based on statistical inference is discussed. The problems of selecting the variables and the number of hidden units are solved by using statistical model selection criteria and tests. Misspecification tests for evaluating an estimated neural network model are considered. Forecasting with neural network models is discussed and an application to a real time series is presented. This paper is a short version of Medeiros, Teräsvirta, and Rech (2006, Journal of Forecasting).
Keywords: Neural networks, model building, forecasting.
5. Medeiros, Marcelo C. and Carlos E. Pedreira (2001). What Are the Effects of Forecasting Linear Time Series with Neural Networks? Engineering Intelligent Systems, 9, 237-242. PDF file
This paper studies the performance of neural networks estimated with Bayesian regularization to model and forecast time series where the data generating process is in fact linear. A simulation experiment is carried out to compare the forecasts made by linear autoregressive models and neural networks.
Keywords: Neural networks, forecasting, misspecification.
4. Medeiros, Marcelo C., Álvaro Veiga and Carlos E. Pedreira (2001). Modelling Exchange Rates: Smooth Transitions, Neural Networks, and Linear Models. IEEE Transactions on Neural Networks, 12, 755-764. PDF file
The goal of this paper is to test for and model nonlinearities in several monthly exchange rates time series. We apply two different nonlinear alternatives, namely: the artificial neural network time series model estimated with Bayesian regularization and a flexible smooth transition specification, called the neuro-coefficient smooth transition autoregression. The linearity test rejects the null hypothesis of linearity in ten out of fourteen series. We compare, using different measures, the forecasting performance of the nonlinear specifications with the linear autoregression and the random walk models.
Keywords: Exchange rate forecasting, smooth transitions, neural networks.
3. Medeiros, Marcelo C., Maurício G. C. Resende and Álvaro Veiga (2001). Piecewise Linear Time Series Estimation with GRASP. Computational Optimization and Applications, 19, 127-144. (PDF version)
This paper describes a heuristic to build piecewise linear statistical models with multivariate thresholds, based on a Greedy Randomized Adaptive Search Procedure (GRASP). GRASP is an iterative randomized sampling technique that has been shown to quickly produce good quality solutions for a wide variety of optimization problems. In this paper we describe a GRASP to sequentially split an n-dimensional space in order to build a piecewise linear time series model.
Keywords: Piecewise-linear models, SETAR models, nonlinearity, GRASP, combinatorial optimization.
2. Medeiros, Marcelo C. and Álvaro Veiga (2000). A Hybrid Linear-Neural Model for Time Series Forecasting. IEEE Transactions on Neural Networks, 11, 1402-1412. (PDF version)
This paper considers a linear model with time varying parameters controlled by a neural network to analyze and forecast nonlinear time series. We show that this formulation, called NCSTAR (Neural Coefficient Smooth Transition AutoRegressive) model, is in close relation to the Threshold AutoRegressive (TAR) model and the Smooth Transition AutoRegressive (STAR) model with the advantage of naturally incorporating linear multivariate thresholds and smooth transitions between regimes. In our proposal, the neural network output is used to induce a partition of the input space, with smooth and multivariate thresholds. This also allows the choice of good initial values for the training algorithm.
Keywords: Nonlinear models, smooth transition, neural networks, multiple regimes.
1. Medeiros, Marcelo C. and C. M. Chaves (1997). Universality in Bootstrap and Diffusion Percolation. Physica A, 234, 604-610, Elsevier Science B. V. (PDF version)
Critical concentrations and exponents of bootstrap and diffusion site-percolation models are presented for the triangular lattice. Results are based on numerical simulations and are consistent with universal exponents for random, bootstrap and diffusion percolation.
Keywords: boostrap and diffusion percolation, triangular lattice.
doi:10.1016/S0378-4371(96)00315-9
Introductions, comments, short papers:
2. Caner, Mehmet and Marcelo C. Medeiros (2016). Model Selection and Shrinkage: An Overview. Econometric Reviews, 35, 1343-1346. (PDF Version).
This special issue is concerned with model selection and shrinkage estimators. This Introduction gives an overview of the papers published in this special issue.
DOI: 10.1080/07474938.2015.1071157
1. Maasoumi, Esfandiar and Marcelo C. Medeiros (2010). The Link Between Statistical Learning Theory and Econometrics: Applications in Economics, Finance and Marketing. Econometric Reviews, 29, 470-475. (PDF version).
Statistical Learning refers to statistical aspects of automated extraction of regularities (structure) in datasets. It is a broad area which includes neural networks, regression-trees, nonparametric statistics and sieve approximation, boosting, mixtures of models, computational complexity, computational statistics, and nonlinear models in general. Although Statistical Learning Theory and Econometrics are closely related, much of the development in each of the areas is seemingly proceeding independently. This special issue brings together these two areas, and is intended to stimulate new applications and appreciation in Economics, Finance, and Marketing. This special volume contains ten innovative papers covering a broad range of relevant topics.
Keywords: Statistical learning theory (machine learning), econometrics, forecasting.
DOI: 10.1080/07474938.2010.481544
Book Chapters:
8. Medeiros, Marcelo C. (2022). Forecasting with Machine Learning Methods. Econometrics with Machine Learning. Felix Chan and Lászlo Mátyás (eds.). Springer, 111–149.
7. Kock, Anders B., Marcelo C. Medeiros, and Gabriel F.R. Vasconcelos (2020). Penalized Time Series Regression. Macroeconomic Forecasting in the Era of Big Data. Peter Fukely (eds.). Springer, 183–228.
6. Burity, Priscilla, Marcelo C. Medeiros, and Luciano Vereda (2014). A Term Structure Model for Defaultable European Sovereign Bonds. Developments in Macro-Finance Yield Curve Modelling. Jagjit S. Chadha, Alain C. J. Durre, Michael A. S. Joyce, and Lucio Sarno (eds.). Cambridge University Press. (PDF version)
To what extent can European sovereign bond yield spreads be attributed to economic fundamentals? In particular, we are interested in the contribution of deficit and debt in the expansion of sovereign spreads in the years after the onset of the current financial and economic crisis that began in 2007. We choose three euro-area countries for this analysis: Spain, Greece and Italy. We note that the country’s own debt has been playing an important role in the recent widening of spreads, especially for Greece and Italy. For Spain, the recent rise in spreads is being driven mainly by variables related to Germany (amongst which German debt is the most important one), and market stress (represented by a high yield index). The response of Greek yield spreads to shocks to national debt and fiscal deficit are stronger than in the case of the other countries analyzed in this work. A shock of one standard deviation in the country’s deficit causes an initial response of the 1 year yield spread of 30% of its standard deviation.
5. Medeiros, Marcelo C. and Eduardo Mendes (2013). Penalized Estimation of Semi-Parametric Additive Time-Series Models. Essays in Nonlinear Time Series Econometrics. Niels Haldrup, Mika Meitz, and Pentti Saikkonen (eds.). Oxford University Press. (PDF version)
This paper studies oracle properties of $\ell_1$-penalized least squares estimator, such as the LASSO, in a semi-parametric regression setting with dependent data. We extend previous results in the literature of semi-parametric models and show that sparsity oracle inequalities for the LASSO also hold in a time-series environment. The results are valid even when the dimension of the model is (much) larger than the sample size and the regression matrix is not positive definite. Our results are derived when the nonparametric component is approximated by a linear combination of known basis functions (sieves), such that the approximating model is linear in the parameters. We advocate the use of a set of randomly generated logistic functions to approximate the nonparametric component of the model. Both simulations and an empirical exercise with Brazilian energy consumption data deliver promising results.
Keywords: penalized estimators, shrinkage, LASSO, semi-parametric models, neural networks, time series, oracle inequalities, energy consumption forecasting.
4. Lee, Tae-Hwy, Eric Hillebrand, and Marcelo C. Medeiros (2013). Bagging Constrained Equity Premium Predictors. Essays in Nonlinear Time Series Econometrics. Niels Haldrup, Mika Meitz, and Pentti Saikkonen (eds.). Oxford University Press. (PDF version)
The literature on excess return prediction has considered a wide array of estimation schemes, among them unrestricted and restricted regression coefficients. We consider bootstrap aggregation (bagging) to smooth parameter restrictions. Two types of restrictions are considered: positivity of the regression coefficient and positivity of the forecast. Bagging constrained estimators can have smaller asymptotic mean-squared prediction errors than forecasts from a restricted model without bagging. Monte Carlo simulations show that forecast gains can be achieved in realistic sample sizes for the stock return problem. In an empirical application using the data set of Campbell, J., and S. Thompson (2008): “Predicting the Equity Premium Out of Sample: Can Anything Beat the Historical Average?”, Review of Financial Studies 21, 1511-1531, we show that we can improve the forecast performance further by smoothing the restriction through bagging. An older version of this paper was circulated under the title “Let’s Do It Again: Bagging Equity Premium Predictors”.
Keywords: Constraints on predictive regression function; Bagging; Asymptotic MSE; Equity premium; Out-of-sample forecasting; Economic value functions.
3. Hillebrand, Eric and Marcelo C. Medeiros (2008). Estimating and Forecasting GARCH Models in the Presence of Structural Breaks and Regime Switches. Forecasting in The Presence of Structural Breaks and Model Uncertainty. Mark Wohar and David Rapach (eds.). Emerald. (PDF version)
In this Chapter, we will outline the statistical consequences of neglecting structural breaks and regime switches in autoregressive and GARCH models and propose two strategies to remedy the problem. The first one is to identify regimes of constant unconditional volatility using a change point detector and estimate a separate GARCH model on the resulting segments. The second approach is to use a multiple-regime GARCH model, such as the Flexible Coefficient GARCH (FCGARCH) specification, where the regime-switches are governed by an observable variable. We will apply both alternatives to an array of financial time series and compare their forecast performance.
2. Medeiros, Marcelo C., Álvaro Veiga, Cristiano Fernandes and Fabiano Oliveira (1999). Extensions of the CAPM. Computation in Economics, Finance and Engineering: Economic Systems. S. Holly e S. A. Greenblatt (eds.). Elsevier Science.
1. Veiga, Álvaro, Marcelo C. Medeiros and Cristiano Fernandes (1998). State Space ARCH: Forecasting Volatility with a Stochastic Coefficient Model. Decision Technologies for Computational Finance: Advances for Computational Management Science. A. P. Refenes, A. N. Burges e J. E. Moody (eds.). Kluwer Academic Publishers, 267-274.
This article investigates the use of AR models with stochastic coefficients to describe the changes in volatility observed in time series of financial returns. Such models can reproduce the main stylised facts observed in financial series: excess kurtosis, serial correlated square returns and time-varying conditional variance. We first cast the model in a state space form. Then the EM algorithm is used to estimate the parameters of the model. With the state-space formulation one can use the Kalman filter to evaluate the conditional variance of future returns. The model is tested using daily returns of TELEBRÁS-PN, one of the main stocks of the brazilian market.
Papers in Brazilian or local journals:
15. Medeiros, Marcelo, Gabriel F. R. Vasconcelos e Eduardo H. de Freitas (2016). Forecasting Brazilian Inflation with High-Dimensional Models. Brazilian Review of Econometrics, 36, 223-254. (PDF version).
In this paper we use high-dimensional models, estimated by the Least Absolute Shrinkage and Selection Operator (LASSO), to forecast the Brazilian inflation. The models are compared to benchmark specifications such as linear autoregressive (AR) and the factor models based on principal components. Our results showed that the LASSO-based specifications have the smallest errors for short-horizon forecasts. However, for long horizons the AR benchmark is the best model with respect to point forecasts, even though there is no significant difference between the forecasts. The factor model also produces some good long horizon forecasts in a few cases. We estimated all the models for the two most important Brazilian inflation measures, the IPCA and the IGP-M indexes. The results also showed that there are differences on the selected variables for both measures. Finally, the most important variables selected by the LASSO based models are, in general, related to government debt and money. On the other hand, variables such as unemployment and production were rarely selected by the LASSO. Therefore, our evidence is against the Phillips curve as the driving mechanism of the Brazilian inflation.
Keywords: Emerging economies, Monetary policy, Brazilian inflation, Forecasting, LASSO, Shrinkage, Model selection.
14. Garcia, Marcio, Marcelo C. Medeiros and Francisco Santos (2016). The High-Frequency Impact of Macroeconomic Announcements in the Brazilian Futures Markets. Brazilian Review of Econometrics, 36, 185-222. (PDF version).
The estimation of the impact of macroeconomic announcements in the Brazilian futures markets is used to uncover the relationship between macroeconomic fundamentals and asset prices. Using intraday data from October 2008 to January 2011, we find that external macroeconomic announcements dominate price changes in the Foreign Exchange and Ibovespa markets, while the impact of the domestic ones is mainly restricted to Interest Rate contracts. We additionally propose an investment strategy based on the conditional price reaction of each market that achieved a success rate of 70% in an out-of-sample study. Finally, we document the impact on volume and bid-ask spreads.
13. Assunção, Juliano, Priscilla Burity and Marcelo C. Medeiros (2015). Is the Convergence of the Manufacturing Sector Unconditional? EconomiA, 16, 273-294. (PDF version).
In Unconditional Convergence, Rodrik (2011) documented that manufacturing industries exhibit unconditional convergence in labor productivity. We provide a novel semi-parametric specification for convergence equations and show that the speed of convergence varies systematically with country-specific characteristics. We consider the flexible smooth transition model with multiple transition variables, which allows each group to have distinct dynamics controlled by a linear combination of known variables. We found evidence that the laws of motion for industry productivity growth are different across countries, varying with political institutions. The speed of convergence also has a non-monotonic relationship with trade openness and education.
12. Garcia, Marcio, Marcelo C. Medeiros and Francisco Santos (2015). Price Discovery in Brazilian FX Markets. Brazilian Review of Econometrics, 35, 65-94. (PDF version).
Brazilian Foreign Exchange (FX) markets have a unique structure: most trades are conducted in the derivatives (futures) market. We study price discovery in the FX markets in Brazil and indicate which market (spot or futures) adjusts more quickly to the arrival of new information. We find that futures market dominates price discovery since it responds for 66.2% of the variation in the fundamental price shock and for 97.4% of the fundamental price composition. In a dynamic perspective, the futures market is also more efficient since, when markets are subjected to a shock in the fundamental price, it is faster to recover to equilibrium. By computing price discovery according to calendar semesters, we find evidence of the correlation between price discovery metrics and market factors, such as spot market supply-demand disequilibrium, central bank interventions and institutional investors’ pressure.
11. Assunção, Juliano, Priscilla Burity and Marcelo C. Medeiros (2015). Unobserved Heterogeneity in Regression Models: A Semiparametric Approach based on Nonlinear Sieves. Brazilian Review of Econometrics, 35, 47-63. (PDF version)
This paper proposes a semiparametric approach to control for unobserved heterogeneity in linear regression models, based on an artificial neural network extremum estimator. We present a procedure to specify the model and use simulations to evaluate its finite sample properties in comparison to alternative methods. The simulations show that our approach is less sensitive to increases in the dimensionality and complexity of the problem. We also use the model to study convergence of per capita income across Brazilian municipalities.
Keywords: Semiparametric models, sieve extremum estimators, neural networks, convergence, unobserved components.
10. Chan, Felix, Michael McAleer and Marcelo C. Medeiros (2015). Structure and asymptotic theory for nonlinear models with GARCH errors. EconomiA, 16, 1-21. (PDF version)
Nonlinear time series models, especially those with regime-switching and/or conditionally heteroskedastic errors, have become increasingly popular in the economics and finance literature. However, much of the research has concentrated on the empirical applications of various models, with little theoretical or statistical analysis associated with the structure of the processes or the associated asymptotic theory. In this paper, we derive sufficient conditions for strict stationarity and ergodicity of three different specifications of the first-order smooth transition autoregressions with heteroskedastic errors. This is essential, among other reasons, to establish the conditions under which the traditional LM linearity tests based on Taylor expansions are valid. We also provide sufficient conditions for consistency and asymptotic normality of the Quasi-Maximum Likelihood Estimator for a general nonlinear conditional mean model with first-order GARCH errors.
Keywords: Nonlinear time series; Regime-switching; Smooth transition; STAR; GARCH; Asymptotic theory
doi: 10.1016/j.econ.2015.01.001
9. Garcia, Marcio, Marcelo C. Medeiros and Francisco Santos (2014). Economic Gains of Realized Volatility in the Brazilian Stock Market. Revista Brasileira de Finanças, 12, 319-349. (PDF version)
This paper evaluates the economic gains associated with following a volatility timing strategy based on a multivariate model of realized volatility. To study this issue, we build a high frequency database with the most actively traded Brazilian stocks. Comparing with traditional volatility methods, we find that, when estimation risk is controlled, economic gains associated with realized measures perform well and increase proportionally to the target return. When expected returns are bootstrapped, however, performance fees are not significant, which is an indication that economic gains of realized volatility are offset by estimation risk.
Keywords: realized volatility; utility; forecasting
8. Medeiros, Marcelo C., Artur M. Passos and Gabriel F. R. Vasconcelos (2014). Parametric Portfolio Selection: Evaluating and Comparing to Markowitz Portfolios. Revista Brasileira de Finanças, 12, 257–284. (PDF version)
In this paper we exploit the parametric portfolio optimization in the Brazilian market. Our data consists of monthly returns of 306 Brazilian stocks in the period between 2001 and 2013. We tested the model both in and out of sample and compared the results with the value and equal weighted portfolios and with a Markowitz based portfolio. We performed statistical inference in the parametric optimization using bootstrap techniques in order to build the parameters empirical distributions. Our results showed that the parametric optimization is a very efficient technique out of sample. It consistently showed superior results when compared with the VW, EW and Markowitz portfolios even when transaction costs were included. Finally, we consider the parametric approach to be very flexible to the inclusion of constraints in weights, transaction costs and listing and delisting of stocks.
Keywords: parametric portfolio; portfolio optimization; portfolio policies.
7. Magri, Rafael and Marcelo C. Medeiros (2013). Nonlinear Error Correction Models with An Application To Commodity Prices. Brazilian Review of Econometrics, 33, 145–170. (PDF version)
Existing tests for nonlinearity in vector error correction models are highly intensive computationally and have nuisance parameters in the asymptotic distribution, what calls for cumbersome bootstrap calculations in order to assess the distribution. Our work proposes a consistent test which is implementable in any statistical package and has Chi-Squared asymptotics. Moreover, Monte Carlo experiments show that in small samples our test has nice size and power properties, often better than the preexisting tests. We also provide a condition under which a two step estimator for the model parameters is consistent and asymptotically normal. Application to international agricultural commodities prices show evidence of nonlinear adjustment to the long run equilibrium on the wheat prices.
Keywords: Cointegration, Nonlinear Models, Linearity Testing, Asymptotic Theory.
6. Areosa, Waldyr and Marcelo C. Medeiros (2007). Inflation Dynamics in Brazil: The Case of a Small Open Economy. Brazilian Review of Econometrics, 27, 131-166. (PDF version)
This paper derives and estimates a structural model for inflation in an open economy. The model represents the standard new-Keynesian Phillips curve (NKPC) and the hybrid curve proposed by Woodford (2003) and Galí and Gertler (1999) as special cases. We present two sets of estimates for the Brazilian economy, initially regarded as a closed economy and then as a small open economy. According to the recent literature, the model contemplates indexation to past inflation and a measure of marginal cost as relevant inflation indicators. Some of the results can be summarized as follows: (i) Brazil, when regarded as a closed economy, has a relatively higher level of nominal rigidity than that of the United States and Europe, and a high level of indexation as well; (ii) In an open economy with indexation, nominal exchange rate appreciation plus foreign inflation affects consumer inflation, and this effect becomes more intense with larger economic openness; (iii) There is a small direct impact of the variables associated with economic openness, with the sum of their coefficients being close to zero; (iv) However, the indirect impact is significant, consistently changing the weights associated with lagged inflation and the expected future inflation.
5. Chrity, Daniel, Márcio G. P. Garcia and Marcelo C. Medeiros (2006). Tendenciosidade do Mercado Futuro de Câmbio: Risco Cambial ou Erros Sistemáticos de Previsão? Revista Brasileira de Finanças, 4, 123-140. (PDF version)
The forward exchange rate is widely used in international finance whenever the analysis of the expected depreciation is needed. It is also used to identify currency risk premium. The difference between the spot rate and the forward rate is supposed to be a predictor of the future movements of the spot rate. This prediction is hardly precise. The fact that the forward rate is a biased predictor of the future change in the spot rate can be attributed to a currency risk premium. The bias can also be attributed to systematic errors of the future depreciation of the currency. This paper analyzes the nature of the risk premium and of the prediction errors in using the forward rate. It will look into the efficiency and rationality of the futures market in Brazil from April 1995 to December 1998.
4. Carvalho, Marcelo R.C., Marco Aurélio S. Freire, Marcelo C. Medeiros and Leonardo R. Souza (2006). Modeling and Forecasting the Volatility of Brazilian Asset Returns: A Realized Variance Approach. Revista Brasileira de Finanças, 4, 321-343. (PDF version)
The goal of this paper is twofold. First, using five of the most actively traded stocks in the Brazilian financial market, this paper shows that the normality assumption commonly used in the risk management area to describe the distributions of returns standardized by volatilities is not compatible with volatilities estimated by EWMA or GARCH models. In sharp contrast, when the information contained in high frequency data is used to construct the realized volatility measures, we attain the normality of the standardized returns, giving promise of improvements in Value-at-Risk statistics. We also describe the distributions of volatilities of the Brazilian stocks, showing that they are nearly lognormal. Second, we estimate a simple model to the log of realized volatilities that differs from the ones in other studies. The main difference is that we do not find evidence of long memory. The estimated model is compared with commonly used alternatives in an out-of-sample forecasting experiment.
3. Souza L., Álvaro Veiga and Marcelo C. Medeiros (2005). Evaluating the Forecasting Performance of GARCH Models Using White’s Reality Check. Brazilian Review of Econometrics, 25, 43-66. (PDF version)
The important issue of forecasting volatilities brings the difficult task of back-testing the forecasting performance. As volatility cannot be observed directly, one has to use an observable proxy for volatility or a utility function to assess the prediction quality. This kind of procedure can easily lead to poor assessment. The goal of this paper is to compare different volatility models and different performance measures using White's Reality Check. The Reality Check consists of a non-parametric test that checks if any of a number of concurrent methods yields forecasts significantly better than a given benchmark method. For this purpose, a Monte Carlo simulation is carried out with four different processes, one of them a Gaussian white noise and the others following GARCH specifications. Two benchmark methods are used: the naive (predicting the out-of-sample volatility by in-sample variance) and the Riskmetrics method.
2. Salgado, Maria José S., Márcio G. P. Garcia and Marcelo C. Medeiros (2005). Monetary Policy During Brazil´s Real Plan: Estimating the Central Bank´s Reaction Function. Revista Brasileira de Economia, 59, 61-79. (PDF version)
This paper uses a Threshold Autoregressive (TAR) model with exogenous variables to explain a change in regime in Brazilian nominal interest rates. By using an indicator of currency crises the model tries to explain the difference in the dynamics of nominal interest rates during and out of a currency crises. The paper then compares the performance of the nonlinear model to a modified Taylor Rule adjusted to Brazilian interest rates, and shows that the former performs considerably better than the latter.
1. Soares, Lacir and Marcelo C. Medeiros (1998). Estimação do lambda Ótimo para Ativos do Mercado Financeiro Brasileiro Através da Metodologia Riskmetrics. Investigação Operacional, 18, 207-213.