Identification of Mixed Causal-Noncausal Models in Finite Samples

Alain Hecq, Lenard Lieb, Sean Telg

Research output: Contribution to JournalArticleAcademicpeer-review


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.
Original languageEnglish
Article number123/124
Pages (from-to)307-331
Number of pages25
JournalAnnals of Economics and Statistics
Publication statusPublished - 2016
Externally publishedYes


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


Dive into the research topics of 'Identification of Mixed Causal-Noncausal Models in Finite Samples'. Together they form a unique fingerprint.

Cite this