Gouriéroux, C., and J.-M. Zakoían [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 captured by 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 identification 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 the LAD estimator that we propose in this paper. Similar to Davis, R., K. Knight, and J. 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, B., F. Breidt, and R. 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 realized volatility measures for 21 equity indexes. The presence of a noncausal component is confirmed in both empirical illustrations. JEL: C22, E37, E44 / KEY WORDS: Noncausal Models, Non-Gaussian Distributions, Realized Volatilities, Bubbles. RÉSUMÉ. Gouriéroux et Zakoïan (2013) ont proposé de modéliser les phénomènes de bulles financières grâce à l'utilisation de modèles de séries temporelles mixtes dits causaux-non causaux. Afin de distinguer un modèle non causal d'un modèle autorégressif standard ou d'une spécification qui englobe ces deux éléments, il est nécessaire de se défaire de l'hypothèse de normalité des erreurs. Toutefois la plupart des variables financières (et dans une large mesure certaines variables macroéconomiques) se caractérisent par des fluctuations grandes et soudaines qui rendent l'utilisation de la distribution Gaussienne peu pertinente. À travers un ensemble de simulations de Monte-Carlo, nous étudions dans cet article la capacité de différents estimateurs (maximum de vraisemblance avec une distribution de Student ainsi qu'un estimateur robuste) à identifier diverses spécifications du modèle mixte à mesure que l'on s'éloigne de la distribution Normale. Nous proposons également une manière simple de calculer les erreurs standards pour ce type de modèles et nous évaluons la pertinence de notre nouvelle approche. Nous illustrons notre méthode sur la demande de panneaux solaires en Belgique ainsi que sur la volatilité de 21 indices composites d'actions. La présence d'une composante non causale est observée dans les deux applications.
The Annals of Economics and Statistics was created in 1969 by Edmond Malinvaud, then director of INSEE (the French National Statistical Institute), under the name Annales de l’INSEE, to publish the research work of INSEE economists. As early as the 1970s, the Annales de l’Insee published articles written by academic economists and econometricians who later became prominent figures in the profession (Olivier Blanchard, Gary Chamberlain, Zvi Griliches, James Heckman, Paul Krugman, Marc Nerlove, to name just a few).
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