Testing constancy of the Hurst exponent of some long memory stationary Gaussian time series

Abstract

Long-range dependence is often observed in stationary time series. The Hurst exponent then characterizes the long term features of the data, which implies that changes in its value could have implications for the long term behaviour of the series. In this paper we propose and apply tests to detect changes over time in the Hurst exponent of long memory Gaussian time series, in particular fractional Gaussian noise and fractionally integrated Gaussian white noise.