Identification of Mixed Causal-Noncausal Models : How Fat Should We Go?

Gouriéroux and Zakoian (2013) propose to use noncausal models to parsimoniously capture nonlinear features 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. This paper investigates by means of simulation how fat the tails of the distribution of the error process have to be such that those models can be identified in practice. We compare the performance of the MLE, assuming a t-distribution, with those of the LAD 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 realized volatility series for 21 equity indexes. The presence of a noncausal component is confirmed in both empirical illustrations.