Temporal aggregation and bandwidth selection in estimating long memory

This paper reinterprets results of Ohanissian et al (2003) to show the asymptotic equivalence of temporally aggregating series and using less bandwidth in estimating long memory by Geweke and Porter-Hudak’s (1983) estimator, provided that the same number of periodogram ordinates is used in both cases. This equivalence is in the sense that their joint distribution is asymptotically normal with common mean and variance and unity correlation. Furthermore, I prove that the same applies to the estimator of Robinson (1995). Monte Carlo simulations show that this asymptotic equivalence is a good approximation in finite samples. Moreover, a real example with the daily US Dollar/French Franc exchange rate series is provided.