Inference on the long-memory properties of time series with non-stationary volatility

•We consider long-memory time series with non-stationary and thus time varying unconditional volatility.•The behavior of the spectral based log-periodogram estimator for the memory parameter is investigated.•It turns out that the estimator is still consistent but its asymptotic variance depends on the volatility scheme of the time series.

Time-varying volatility is often present in time series data and can have adverse effects when inferring about the persistence properties of examined series. This note analyzes the effects of such nonstationarity on periodogram-based inference for the fractional integration parameter. Based on asymptotic arguments and Monte Carlo simulations, we show that the log-periodogram regression estimator remains consistent, but has asymptotic distribution whose variance depends on the variation of the volatility of the series.