Testing for Long Memory in Potentially Nonstationary Perturbed Fractional Processes

Abstract

In this paper, we propose new tests for long memory in stationary and nonstationary time series possibly perturbed by short-run noise which may be serially correlated. The tests are all based on semiparametric estimators and exploit the self-similarity property of long memory processes. We offer simulation results that show good size properties of the tests, with power against spurious long memory. An empirical study of daily log-squared returns series of exchange rates and DJIA30 stocks shows that indeed there is long memory in exchange rate volatility and stock return volatility.

Keywords: Temporal aggregation, semiparametric estimation, fractional integration, self-similarity, perturbed fractional processes

JEL Classification: C14, C22, C43