On the Finite-Sample Biases in Nonparametric Testing for Variance Constancy

Resumen

In this paper we analyse the small-sample size distortions of nonparametric CUSUM tests for variance stability resulting from the long-run variance estimation. The long-run variance estimator is a key factor necessary to ensure asymptotically pivotal test statistics. We discuss the large sample properties of these tests under standard and recently developed fixed- b bandwidth asymptotic theory for kernel heteroskedasticity and autocorrelation consistent (HAC) estimators, and analyse the finite sample performance for different data generation processes of major empirical relevance. Despite the good properties evidenced by the large-sample theory, important distortions may arise when the empirical processes exhibit strongly-persistent volatility and excess kurtosis even in relatively large samples. In this context, consistent (inconsistent) HAC estimators may lead to over-sized (under-sized) tests. Hence, nonparametric tests may lack power to distinguish between a strongly persistent -yet stationary- process and a process with a structural break.