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

Giancaterini, Francesco; Hecq, Alain

This paper analyzes the properties of the Maximum Likelihood Estimator for mixed causal and noncausal models when the error term follows a Student's t-distribution. In particular, we compare several existing methods to compute the expected Fisher information matrix and show that they cannot be applied in the heavy-tail framework. For this purpose, we propose a new approach to make inference on causal and noncausal parameters in finite sample sizes. It is based on the empirical variance computed on the generalized Student's t, even when the population variance is not finite. Monte Carlo simulations show the good performances of our new estimator for fat tail series. We illustrate how the different approaches lead to different standard errors in four time series: annual debt to GDP for Canada, the variation of daily Covid-19 deaths in Belgium, the monthly wheat prices and the monthly inflation rate in Brazil.