PROPERTIES OF THE SAMPLE AUTOCORRELATIONS IN AUTOREGRESSIVE STOCHASTIC VOLATlLITY MODELS

Abstract

Time series generated by Stochastic Volatility (SV) processes are uncorrelated although not independent. This has consequences on the properties of the sample autocorrelations. In this paper, we analyse the asymptotic and finite sample properties of the correlogram of series generated by SV processes. It is shown that the usual uncorrelatedness tests could be misleading. The properties of the correlogram of the log-squared series, often used as a diagnostic of conditional heteroscedasticity, are also analysed. It is proven that the more persistent and the larger the variance of volatility, the larger the negative bias of fue sample autocorrelations of that series.