Semiparametric estimation of long-memory volatility dependencies: The role of high-frequency data

Recent empirical studies have argued that the temporal dependencies in financial market volatility are best characterized by long memory, or fractionally integrated, time series models. Meanwhile, little is known about the properties of the semiparametric inference procedures underlying much of this empirical evidence. The simulations reported in the present paper demonstrate that, in contrast to log-periodogram regression estimates for the degree of fractional integration in the mean (where the span of the data is crucially important), the quality of the inference concerning long-memory dependencies in the conditional variance is intimately related to the sampling frequency of the data. Some new estimators that succinctly aggregate the information in higher frequency returns are also proposed. The theoretical findings 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.