Semiparametric Estimation of Long-Memory Volatility Dependencies

Recent empirical studies have argued that the temporal dependencies in "nancialmarket volatility are best characterized by long memory, or fractionally integrated, timeseries models. Meanwhile, little is known about the properties of the semiparametric inference procedures underlying much of this empirical evidence. The simulations reportedin the present paper demonstrate that, in contrast to log-periodogram regressionestimates for the degree of fractional integration in the mean (where the span of the datais crucially important), the quality of the inference concerning long-memory dependenciesin the conditional variance is intimately related to the sampling frequency of the data. Somenew estimators that succinctly aggregate the information in higher frequency returns arealso proposed. The theoretical "ndings are illustrated through the analysis of a ten-year time series consisting of more than half-a-million intradaily observations on the Japanese Yen U.S. Dollar exchange rate.