Long-memory in high-frequency exchange rate volatility under temporal aggregation

This paper applies log-periodogram estimators of the fractional difference parameter to the volatility of the US dollar exchange rate returns of 11 European currencies, and under temporal aggregation from an underlying half-hourly intra-day frequency. Particular attention is paid to the sequencing of the nonlinear transformation of returns and their temporal aggregation. The results reported confirm that long-memory in absolute returns constitutes an intrinsic and empirically significant characteristic of the exchange rates considered. At the practical level, our results lend support to the proposal that nonlinear transformation prior to temporal aggregation can return meaningful long-memory parameter estimates. Our findings also illustrate the advantages of long-memory parameter estimation based on the smoothed periodogram applied to absolute returns in controlling for noise induced by temporal aggregation in the processing of high-frequency data.