  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.
