Inference on the Long-Memory Properties of Time Series with Non-Stationary Volatility

Many time series exhibit unconditional heteroskedasticity, often in addition to conditional one. But such time-varying volatility of the data generating process can have rather adverse effects when inferring about its persistence; e.g. unit root and stationarity tests possess null distributions depending on the so-called variance profile. On the contrary, this is guaranteed if taking protective actions as simple as using White standard errors (which are employed anyway to deal with conditional heteroskedasticity). The paper explores the influence of time-varying volatility on fractionally integrated processes. Concretely, we discuss how to model long memory in the presence of time-varying volatility, and analyze the effects of such nonstationarity on several existing inferential procedures for the fractional integration parameter. Based on asymptotic arguments and Monte Carlo simulations, we show that periodogram-based estimators, such as the local Whittle or the log-periodogram regression estimator, remain consistent, but have asymptotic distributions whose variance depends on the variance profile. Time-domain, regression-based tests for fractional integration retain their validity if White standard errors are used. Finally, the modified range-scale statistic is only affected if the series require adjustment for deterministic components.