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, forthcoming. (PDF version)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. Supplemental materials for this article are available. 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 version)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.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 version).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 version).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. 39. Medeiros, Marcelo C. and Eduardo F. Mendes (2017). Adaptive Lasso estimation for ARDL models with GARCH innovations. Econometric Reviews, 36, 622-637. (PDF version)IIn 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.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 version). 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.
37. Berriel, Tiago C., Marcelo C. Medeiros and Marcelo Sena (2016). 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.
doi: 10.1016/j.econlet.2016.05.032 36. Medeiros, Marcelo C. and Gabriel Vasconcelos (2016). 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.
doi: 10.1016/j.econlet.2015.11.017 35. Medeiros, Marcelo C. and Eduardo F. Mendes (2016). _{1}-Regularization of High-dimensional Time-Series Models with Flexible Innovations"). Journal of Econometrics, 191, 255-271. (PDF version).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). Keywords: Smooth transitions, long memory, forecasting, realized variance.doi:10.1080/07350015.2014.985828
33. Fernandes, Marcelo, Marcelo C. Medeiros, and Alvaro Veiga (2016). 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).
doi:10.1016/j.jbankfin.2013.11.004
31. Medeiros, Marcelo C., Eduardo Mendes, and Les Oxley (2014). 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.
30. Hillebrand, Eric, Marcelo C. Medeiros, and Junyue Xu (2013).
29. Asai, Manabu, Michael McAleer, and Marcelo C. Medeiros (2012).
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. doi: 10.1093/jjfinec/nbr015
28. Asai, Manabu, Michael McAleer, and Marcelo C. Medeiros (2012). Keywords: realized volatility; diffusion; financial
econometrics; measurement errors; forecasting; model evaluation;
goodness-of-fit. 27. Preve, Daniel and Marcelo C. Medeiros. 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). 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).
24. McAleer, Michael and Marcelo C. Medeiros (2011). Forecasting Realized Volatility with Linear and Nonlinear Models. Journal of Economic Surveys, 25, 6-18. (PDF version).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 version). 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. 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 version).Keywords: Fuzzy models, linearity testing, time series. doi: 10.1016/j.fss.2010.01.005 21. Hillebrand, Eric and Marcelo C. Medeiros (2010).
doi:10.1080/07474938.2010.481554
20. Scharth, Marcel and Marcelo C. Medeiros (2009).
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 version) 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.
18. Medeiros, Marcelo C., Michael McAleer, Daniel Slottje, Vicente Ramos and Javier Rey-Maquieira (2008).
doi:10.1016/j.jeconom.2008.09.018 17. McAleer, Michael, Marcelo C. Medeiros, Daniel Slottje (2008).
doi:10.1016/j.jeconom.2008.09.031 16. McAleer, Michael and Marcelo C. Medeiros (2008).
doi:10.1016/j.jeconom.2008.09.032 15. Soares, Lacir and Marcelo C. Medeiros (2008).
doi:10.1016/j.ijforecast.2008.08.003
14. Joel C. da Rosa, Alvaro Veiga, and Marcelo C. Medeiros (2008).
doi:10.1016/j.csda.2007.08.018
13. McAleer, Michael and Marcelo C. Medeiros (2008).
doi: 10.1080/07474930701853509
12. Medeiros, Marcelo C., Timo Teräsvirta and Gianluigi Rech (2006).
11. Teräsvirta, Timo, Dick van Dijk and Marcelo C. Medeiros (2005).
doi:10.1016/j.ijforecast.2005.04.010
10. Medeiros, Marcelo C. and Álvaro Veiga (2005).
9. Suarez-Fariñas, Mayte, Carlos E. Pedreira and Marcelo C. Medeiros (2004).
doi: 10.1198/016214504000001691
8. Medeiros, Marcelo C., and Álvaro Veiga (2003).
7. Medeiros, Marcelo C., Álvaro Veiga and Maurício G. C. Resende (2002).
doi:10.1198/106186002317375712
6. Medeiros, Marcelo C. and Timo Teräsvirta (2001).
5. Medeiros, Marcelo C. and Carlos E. Pedreira (2001).
4. Medeiros, Marcelo C., Álvaro Veiga and Carlos E. Pedreira (2001).
3. Medeiros, Marcelo C., Maurício G. C. Resende and Álvaro Veiga (2001).
2. Medeiros, Marcelo C. and Álvaro Veiga (2000).
1. Medeiros, Marcelo C. and C. M. Chaves (1997).
doi:10.1016/S0378-4371(96)00315-9
2. Caner, Mehmet and Marcelo C. Medeiros (2016). 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).
doi: 10.1080/07474938.2010.481544
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). 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.
4. Lee, Tae-Hwy, Eric Hillebrand, and Marcelo C. Medeiros (2013). 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). 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).
1. Veiga, Álvaro, Marcelo C. Medeiros and Cristiano Fernandes (1998). 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.
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 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.
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 theory9. Garcia, Marcio, Marcelo C. Medeiros and Francisco Santos (2014). 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; forecasting8. Medeiros, Marcelo C., Artur M. Passos and Gabriel F. R. Vasconcelos (2014). Keywords: parametric portfolio; portfolio optimization; portfolio policies.
7. Magri, Rafael and Marcelo C. Medeiros (2013). 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).
5. Chrity, Daniel, Márcio G. P. Garcia and Marcelo C. Medeiros (2006).
4. Carvalho, Marcelo R.C., Marco Aurélio S. Freire, Marcelo C. Medeiros and Leonardo R. Souza (2006).
3. Souza L., Álvaro Veiga and Marcelo C. Medeiros (2005).
2. Salgado, Maria José S., Márcio G. P. Garcia and Marcelo C. Medeiros (2005).
1. Soares, Lacir and Marcelo C. Medeiros (1998). |