Long Memory, Spurious Memory: Persistence in Range-Based Volatility of Exchange Rates

Abstract

This study considers the long memory and fractional integration in the range-based volatilities across 30 currencies against USD. Graphical analysis of the autocorrelation function at long lags and pole near zero frequencies in the periodogram suggests the existence of fractional integration. We apply semi-parametric methods to measure long-range dependence. We find a decrease in the memory estimates with an increase in the bandwidth, which indicates the presence of spurious memory rather true long memory. The hypothesis of long memory against the alternative of spurious memory is also tested by applying the different semi-parametric methods. Empirical results confirm the presence of spurious memory that may be a result of some shocks to the volatility estimator. Furthermore, the reduced memory estimates obtained by utilising an estimator accounting for level shifts also explains the inconsistency of the Local Whittle estimator. We also estimate the number of breaks for each series.