Abstracts

Bovas ABRAHAM, University of Waterloo, Ontario, Canada

TITLE OF THE TALK: GEORGE BOX: AN ACCIDENTAL STATISTICIAN WHO TRANSFORMED TIME SERIES ANALYSIS

Summary: George Edward Pelham Box was born on October 19, 1919 in Gravesend, Kent, England and died on March 28, 2013 in Madison, Wisconsin. George Box was one of the world’s most leading statisticians and made path breaking contributions to many areas of statistics including design of experiments, robustness, Bayesian methods, time series analysis and forecasting, and quality improvement. This talk discusses his contributions to time series analysis and forecasting. His work in this area started in collaboration with Gwilym Jenkins in the early 1960’s and continued over the next several decades. His contributions include the classic and extraordinarily influential book “Time Series Analysis: Forecasting and Control” written with Gwilym Jenkins and first published by Holden Day in 1970. His subsequent contributions to time series analysis include joint work with George Tiao and many former graduate students including this one. His work provided a unified framework for carrying out time series analysis in practice and laid the foundation for many new developments in the field.

In this discourse, I will discuss many significant developments in time series analysis including ARIMA models and the time series modeling strategy proposed by Box and Jenkins (1970), along with a discussion of their contributions to forecasting. We will consider the use of these models for assessing the impact of external interventions as described by Box and Tiao (1975). Extensions of this approach to detect outliers will also be considered (for example, Abraham and Box (1979)). Box and Newbold (1971) commented on spurious correlations in the context of correlating non-stationary time series, and Box and Tiao (1977) discussed canonical analysis of multiple time series. The ideas in these two papers laid the foundation for the work on co-integration by Rob Engle and Clive Granger who won the Nobel Prize in Economics in 2003. George Box’s work has had a great impact on the theory and practice of time series analysis.

Taoufik BOUEZMARNI, Université de Sherbrooke, Canada

TITLE OF THE TALK: NONPARAMETRIC BETA KERNEL ESTIMATOR FOR LONG MEMORY TIME SERIES

Summary: This paper introduces a new nonparametric estimator of the spectral density that is given by smoothing the periodogram by beta kernel density. The estimator is proved to be bounded for short memory data and diverges at the origin for long memory data. The convergence, in probability, of the relative error and Monte Carlo simulations show that the estimator automatically adapts to the long- or the short-range dependency of the process. A cross-validation procedure is also studied in order to select the nuisance parameter of the estimator. Illustrations on historical as well as most recent returns and absolute returns of the S&P500 index show the reasonable performance of the estimation and show that the data-driven estimator is a valuable tool for the detection of long-memory as well as hidden periodicities in stock returns. (Joint work with Sébastien Van Bellegem (CORE, UCL, Belgiun) and Yassir Rabhi (Université de Sherbrooke))

Chafik BOUHADDIOUI, United Arab Emirates University, UAE

TITLE OF THE TALK: GENERALIZED TESTS OF CAUSALITY BETWEEN TWO VECTOR AUTOREGRESSIVE SERIES

Summary: We propose a test for non-causality at various horizons for infinite-order vector autoregressive. We first introduce multiple horizon infinite-order vector autoregressions which can be approximated by a multiple horizon finite-order vector autoregressions. The order is assumed to increase with the sample size. Under some regularity conditions, we study the estimation of parameters obtained from the approximation of the infinite-order autoregression by a finite-order autoregression. The test can be implemented simply through linear regression methods and do not involve the use of artificial simulations. The asymptotic distribution of the new test statistic is derived under the hypothesis of non-causality at various horizons. An asymptotic power of the test will be studied. Bootstrap procedures are also considered. The methods are applied to a VAR model of the US economy.

Mohamed CHAOUCH, United Arab Emirates University, UAE

TITLE OF THE TALK: CONDITIONAL VARIANCE ESTIMATION IN HETEROSCEDASTIC FUNCTIONAL REGRESSION MODEL WITH MARTINGALE DIFFERENCE ERRORS

Summary: This paper aims to study the asymptotic properties of the conditional variance estimator in a nonlinear heteroscedastic functional regression model with martingale difference errors . A kernel-type estimator of the conditional variance is introduced when the response is a real-valued random variable and the covariate takes values in an infinite dimensional space endowed with a semi-metric. Under stationarity and ergodicity assumptions, a uniform almost sure consistency rate as well as the asymptotic distribution of the estimator is established. To build confidence intervals for the conditional variance, two approaches are discussed. The first one is a normal approximation-based approach and the second applies empirical likelihood method. We stress on the fact that errors are assumed to form a martingale difference and may depend on the covariate. Moreover, our results hold under a general dependency structure (ergodicity)and without assuming any mixing conditions, which allow to cover a larger class of dependent processes. A simulation study is carried out to show the performance of the proposed estimator. An application to volatility prediction of daily IBM asset price using intraday (one minute frequency) S&P500 index curves is also provided.

Sophie DABO-NIANG, University of Lille, France

TITLE OF THE TALK: FUNCTIONAL SPATIAL AUTOREGRESSIVE MODELS

Summary: A functional linear autoregressive spatial model, where the explanatory variable takes values in a function space while the response process is real-valued and spatially autocorrelated, is proposed. The specificity of the model is due to the functional nature of the explanatory variable and the structure of a spatial weight matrix that defines the spatial dependency between neighbors. The estimation procedure consists of reducing the infinite dimension of the functional explanatory variable and maximizing the quasi-maximum likelihood. We establish the consistency of the estimate. The ability of the methodology is illustrated via simulations and by application to real data.

Jean-Marie DUFOUR, McGill University, Canada

TITLE OF THE TALK: WEAK BETA, STRONG BETA: MULTI-FACTOR PRICING AND RANK RESTRICTIONS

Summary: A plethora of competing factors appear to explain the cross section of expected returns, as recent methodological works in asset pricing call for raising statistical standards. This paper contributes to this literature via an identification-robust methodology to assess factor pricing, regardless of whether factor betas are jointly informative or not, or heterogenous enough to identify risk premiums. We provide a formal definition of non-informative factors in this regard, and document the extent to which inferences on Fama-French-Carhart factors are affected by taking into account such source of uncertainty. Confidence sets are proposed that invert popular asset pricing tests, and analytical and tractable solutions are derived. An extensive simulation study is reported in addition to our empirical assessment of the standard as well as the recent profitability and investment factors. Results suggest that the standard three factors are not statistically insignificant, yet resulting betas are not convincingly priced. Evidence of pricing weakens post 1970s, as the three factor model more broadly does not perform well. We do not find evidence favouring size or book-to-market risk over the market risk. The Carhart and recent Fama-French factors are not utterly redundant, yet heterogeneity of betas is not sufficient to distinguish a priced momentum anomaly from profitability or investment risk. All models struggle when tested with all portfolios jointly and identification of risk premium worsens globally post 2000s. (Joint work with Marie-Claude Beaulieu, Université Laval, Quebec city, Canada and Lynda Khalaf, Carleton University, Ottawa, Canada)

Ahmed EL GHINI, Mohammed V University in Rabat, Morocco

TITLE OF THE TALK: TESTING CONTAGION AND SPILLOVER EFFECTS IN FINANCIAL MARKETS BASED ON MULTIVARIATE GARCH MODELS

Summary: TBA

Ali GHODSI, University of Waterloo, Ontario, Canada

TITLE OF THE TALK: DETECTING CHANGE-POINTS IN TIME SERIES BY MAXIMUM MEAN DISCREPANCY OF ORDINAL PATTERN DISTRIBUTIONS

Summary: As a new method for detecting change-points in high-resolution time series, we apply Maximum Mean Discrepancy to the distributions of ordinal patterns in different parts of a time series. The main advantage of this approach is its computational simplicity and robustness with respect to (non-linear) monotonic transformations, which makes it particularly well-suited for the analysis of long biophysical time series where the exact calibration of measurement devices is unknown or varies with time. We establish consistency of the method and evaluate its performance in simulation studies. Furthermore, we demonstrate the application to the analysis of economic data, electroencephalography (EEG) and electrocardiography (ECG) recordings. (Joint work with Mathieu Sinn, IBM Research Dublin, Ireland and Karsten Keller, Institute of Mathematics University of Lubeck, Lubeck, Germany)

Kilani GHOUDI, United Arab Emirates University, UAE

TITLE OF THE TALK: EMPIRICAL PROCESSES BASED ON RESIDUALS AND THEIR APPLICATIONS IN MODEL DIAGNOSTICS

Summary: The talk introduces empirical processes based on residuals of time series/regression models. Asymptotic properties of univariate and multivariate empirical processes will first be discussed. Empirical copula processes based on residuals/squared residuals are also derived. Applications to model diagnostics (goodness of fit, change point analysis and tests of independence) will also be discussed with limitations and complications pointed out.

Guy MELARD, Université Libre de Bruxelles, Belgique

TITLE OF THE TALK: NUMERICAL PROBLEMS IN TIME SERIES ANALYSIS

Summary: First, we discuss numerical problems around autocorrelations of autoregressive-moving average (ARMA) processes. Computation of these autocorrelations is needed in maximum likelihood estimation of ARMA and vector ARMA models but also to derive a Wiener-Kolmogorov filter, or to check for stationarity and invertibility. Problems occur when there are too many common roots.

Second, we examine nonlinear estimation which is heavily used in time series analysis, e.g. to estimate the parameters of an ARMA model by quasi maximum likelihood. We focus especially on the derivation of the standard errors. We start by comparing on that respect several statistical packages (some R packages, SPSS, SAS, Stata, …, and our own Time Series Expert) on given datasets. Then we discuss the various algorithms that can be used to derive the Fisher information matrix from the results of an optimization algorithm and comment on the numerical problems that can arise.

Giovanni MEROLA, Xi'an Jioatong Liverpool University, Suzhou, China

TITLE OF THE TALK: ANALYSIS OF THE CHINESE FUTURES MARKET USING HIGH-FREQUENCY TRADING DATA

Summary: Futures contracts have become a new widely traded assets class for portfolio investors and now represent a valid investment diversification instrument. The large inflow integrated the previously segmented commodity markets with each other and with outside financial markets changing the traditional correlation structure among different types of commodities. We will discuss the correlation structure of different segments of the futures market in China using principal components analysis on 5-minute returns. The analysis of these data is made difficult by the presence of a large proportion of zero returns. We propose to use within period returns to estimate the volatility. We show that financial indices futures have a weak correlation with commodity futures.

Bouchra NASRI, HEC Montréal, Canada

TITLE OF THE TALK: ON COPULA-BASED CONDITIONAL QUANTILE ESTIMATORS

Summary: Recently, two different copula-based approaches have been proposed to estimate the conditional quantile function of a variable Y with respect to a vector of covariates X: the first estimator is related to quantile regression weighted by the conditional copula density, while the second estimator is based on the inverse of the conditional distribution function written in terms of margins and the copula. Using empirical processes, we show that even if the two estimators look quite different, their estimation errors have the same limiting distribution. Also, we propose a bootstrap procedure for the limiting process in order to construct uniform confidence bands around the conditional quantile function. A case study based on daily exchange rate series illustrates the proposed methodology.

Kaveh SALEHZADEH-NOBARI, Business School, Durham University, UK

TITLE OF THE TALK: EXECUTIVE CONSTRAINTS AND STOCK VOLATILITY IN THE MENA REGION

Summary: This paper studies the impact of executive constraints on the volatility and the risk of listed MENA region firms. Using a two-step estimation approach, we first measure and test the impact of a proxy of executive constraints on the ratio of idiosyncratic volatility to the systematic volatility of 2,330 firms, that belong to 12 countries in the MENA region for the period spanning from 1996 to 2014. Thereafter, we examine the impact of executive constraints on the firms' performance, where the latter is measured using some upper and lower quantiles of the firms' return distributions. Finally, we assess the predictability power of executive constraints on the future returns and examine whether in the presence of predictability power, this measure is of economic value to an investor who makes capital allocation choices. Our empirical results indicate a clear negative impact of the executive constraints on the ratio of idiosyncratic volatility to the systematic volatility, and predictability on future returns is found in the fifth horizon, which corresponds to governmental/presidential cycles.

Abderrahim TAAMOUTI, Business School, Durham University, UK

TITLE OF THE TALK: Measuring Local Heteroskedasticity, What Can we Learn from the Heterogeneity in the Heteroskedasticity?

Summary: We introduce a new measure to quantify/test the strength of heteroskedasticity at each point (quantile) of the conditional distribution of a random variable conditional on the support or a sub-support of other random variables. We can argue that tracing out the path of the degree of heteroskedasticity across different ranges of the conditioning variables might be informative about the underlying model that links the variables of interest. Our measure of local heteroskedasticity is based on nonparametric quantile regressions and is expressed in terms of unrestricted and restricted expectations of quantile loss functions. It can be consistently estimated by replacing the unknown expectations by their nonparametric estimates. We derive a Bahadur-type representation for the nonparametric estimator of the measure. We provide the asymptotic distribution of this estimator, which one can use to build tests for the statistical significance of the measure. Thereafter, we establish the validity of a fixed-regressor bootstrap that one can use infinite sample settings to perform tests. A Monte Carlo simulation study reveals that the bootstrap-based test has a good finite sample size and power for a variety of data generating processes and different sample sizes. Finally, two empirical applications are provided to illustrate the importance of the proposed measure. (Joint work with Xiaojun Song, Peking University)

Aera THAVANESWARAN, University of Manitoba, Canada

TITLE OF THE TALK: ESTIMATING FUNCTIONS APPROACH FOR DURATION MODELS

Summary: Accurate modeling of patterns in inter-event durations is of considerable interest in high-frequency financial data analysis. The class of logarithmic autoregressive conditional duration (Log ACD) models provides a rich framework for analyzing durations, and recent research is focused on developing fast and accurate methods for fitting these models to long time series of durations under least restrictive assumptions. This talk describes an optimal semi-parametric modeling approach using martingale estimating functions. This approach only requires assumptions on the first few conditional moments of the durations and does not require specification of the probability distribution of the process. We introduce three approaches for parameter estimation in our methodology, including solution of nonlinear estimating equations, recursive formulas for the vector-valued parameter estimates, and iterated component-wise scalar recursions. All three estimation methods are compared. Effective starting values from an approximating time series model increase the accuracy of the final estimates.