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Identification of Mixed Causal-Noncausal Models in Finite Samples

Author

Listed:
  • Alain Hecq
  • Lenard Lieb
  • Sean Telg

Abstract

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.

Suggested Citation

  • Alain Hecq & Lenard Lieb & Sean Telg, 2016. "Identification of Mixed Causal-Noncausal Models in Finite Samples," Annals of Economics and Statistics, GENES, issue 123-124, pages 307-331.
  • Handle: RePEc:adr:anecst:y:2016:i:123-124:p:307-331
    DOI: 10.15609/annaeconstat2009.123-124.0307
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    Citations

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    Cited by:

    1. Fries, Sébastien & Zakoian, Jean-Michel, 2017. "Mixed Causal-Noncausal AR Processes and the Modelling of Explosive Bubbles," MPRA Paper 81345, University Library of Munich, Germany.
    2. Hecq, Alain & Issler, João Victor & Telg, Sean, 2017. "Mixed Causal-Noncausal Autoregressions with Strictly Exogenous Regressors," MPRA Paper 80767, University Library of Munich, Germany.
    3. Alain Hecq & Sean Telg & Lenard Lieb, 2017. "Do Seasonal Adjustments Induce Noncausal Dynamics in Inflation Rates?," Econometrics, MDPI, Open Access Journal, vol. 5(4), pages 1-22, October.
    4. Cubadda, Gianluca & Hecq, Alain & Telg, Sean, 2017. "Detecting Co-Movements in Noncausal Time Series," MPRA Paper 77254, University Library of Munich, Germany, revised 02 Mar 2017.

    More about this item

    Keywords

    Noncausal Models; Non-Gaussian Distributions; Realized Volatilities; Bubbles;

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • E37 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Forecasting and Simulation: Models and Applications
    • E44 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Financial Markets and the Macroeconomy

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