Testing for vector autoregressive dynamics under heteroskedasticity

Abstract

In this paper we introduce a bootstrap procedure to test parameterrestrictions in vector autoregressive models which is robust incases of conditionally heteroskedastic error terms. The adoptedwild bootstrap method does not require any parametricspecification of the volatility process and takes contemporaneouserror correlation implicitly into account. Via a Monte Carloinvestigation empirical size and power properties of the newmethod are illustrated. We compare the bootstrap approach withstandard procedures either ignoring heteroskedasticity or adoptinga heteroskedasticity consistent estimation of the relevantcovariance matrices in the spirit of the White correction. Interms of empirical size the proposed method clearly outperformscompeting approaches without paying any price in terms of sizeadjusted power. We apply the alternative tests to investigate thepotential of causal relationships linking daily prices of naturalgas and crude oil. Unlike standard inference ignoring time varyingerror variances, heteroskedasticity consistent test procedures donot deliver any evidence in favor of short run causality betweenthe two series.Energy markets;Causality;Bootstrap;Heteroskededasticity;Hypothesis testing;Vector autoregression