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

TL;DR

This paper introduces a novel inference method for mixed causal and noncausal models with heavy-tailed generalized Student's t errors, effective in finite samples and demonstrated through empirical applications.

Contribution

A new variance-based inference approach for heavy-tailed models that does not rely on population variance, applicable to finite samples.

Findings

The new variance method performs well in fat-tailed series.

Monte Carlo simulations confirm the method's robustness.

Empirical applications demonstrate practical utility.

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.