Abstract:
Recent empirical studies have argued that the temporal dependencies in "nancial
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 "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.
