1. Identification of Mixed Causal-Noncausal Models in Finite Samples
- Author
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Lenard Lieb, Alain Hecq, Sean Telg, QE Econometrics, RS: GSBE EFME, Macro, International & Labour Economics, and RS: GSBE ETBC
- Subjects
Statistics and Probability ,Economics and Econometrics ,Realized variance ,Non-Gaussian distributions ,Monte Carlo method ,Single Equation Models ,Single Variables: Time-Series Models ,Dynamic Quantile Regressions ,Dynamic Treatment Effect Models ,Asymptotic distribution ,Noncausal models ,01 natural sciences ,Normal distribution ,Business Fluctuations ,bubbles ,010104 statistics & probability ,0502 economics and business ,Econometrics ,e37 - Prices ,0101 mathematics ,050205 econometrics ,Mathematics ,and Cycles: Forecasting and Simulation: Models and Applications ,e37 - Prices, Business Fluctuations, and Cycles: Forecasting and Simulation: Models and Applications ,Prices ,Series (mathematics) ,05 social sciences ,Estimator ,Financial Markets and the Macroeconomy ,Autoregressive model ,e44 - Financial Markets and the Macroeconomy ,Kurtosis ,Statistics, Probability and Uncertainty ,c22 - "Single Equation Models ,Dynamic Treatment Effect Models" ,Social Sciences (miscellaneous) ,Realized volatilities - Abstract
Gouriéroux and Zakoïan (2013) propose to use noncausal models to parsimoniously capture nonlinear features often observed in financial time series and in particular bubble phenomena. In order to distinguish causal autoregressive processes from purely noncausal or mixed causal-noncausal ones, one has to depart from the Gaussianity assumption on the error distribution. Financial (and to a large extent macroeconomic) data are characterized by large and sudden changes that cannot be capturedby the Normal distribution, which explains why leptokurtic error distributions are often considered in empirical finance. By means of Monte Carlo simulations, this paper investigates the identication of mixed causal-noncausal models in finite samples for different values of the excess kurtosis of the error process. We compare the performance of the MLE, assuming a t-distribution, with that of theLAD estimator that we propose in this paper. Similar to Davis, Knight and Liu (1992) we find that for infinite variance autoregressive processes both the MLE and LAD estimator converge faster. We further specify the general asymptotic normality results obtained in Andrews, Breidt and Davis (2006)for the case of t-distributed and Laplacian distributed error terms. We first illustrate our analysis by estimating mixed causal-noncausal autoregressions to model the demand for solar panels in Belgium over the last decade. Then we look at the presence of potential noncausal components in daily realizedvolatility measures for 21 equity indexes. The presence of a noncausal component is confirmed in both empirical illustrations.
- Published
- 2016