Inference in mixed causal and noncausal models with generalized Student’s t-distributions

Abstract

The properties of Maximum Likelihood estimator in mixed causal and noncausal models with a generalized Student’s $t$ error process are reviewed. Several known existing methods are typically not applicable in the heavy-tailed framework. To this end, a new approach to make inference on causal and noncausal parameters in finite sample sizes is proposed. It exploits the empirical variance of the generalized Student’s $t$, without the existence of population variance. Monte Carlo simulations show a good performance of the new variance construction for fat tail series. Finally, different existing approaches are compared using three empirical applications: the variation of daily COVID-19 deaths in Belgium, the monthly wheat prices, and the monthly inflation rate in Brazil.