Orthogonal Impulse Response Analysis in Presence of Time-Varying Covariance

TL;DR

This paper introduces a new method for analyzing orthogonal impulse response functions when the covariance of errors varies over time, improving accuracy over traditional sub-period approaches.

Contribution

It proposes a novel averaging approach of Cholesky decompositions of nonparametric covariance estimators for better time-varying OIRF analysis.

Findings

The new method reduces bias compared to standard sub-period analysis.

Monte Carlo simulations validate the theoretical properties.

Application to U.S. inflation and oil shocks demonstrates practical relevance.

Abstract

In this paper the orthogonal impulse response functions (OIRF) are studied in the non-standard, though quite common, case where the covariance of the error vector is not constant in time. The usual approach for taking into account such behavior of the covariance consists in applying the standard tools to sub-periods of the whole sample. We underline that such a practice may lead to severe upward bias. We propose a new approach intended to give what we argue to be a more accurate resume of the time-varying OIRF. This consists in averaging the Cholesky decomposition of nonparametric covariance estimators. In addition an index is developed to evaluate the heteroscedasticity effect on the OIRF analysis. The asymptotic behavior of the different estimators considered in the paper is investigated. The theoretical results are illustrated by Monte Carlo experiments. The analysis of the orthogonal response functions of the U.S. inflation to an oil price shock, shows the relevance of the tools proposed herein for an appropriate analysis of economic variables.