Pooled Log Periodogram Regression

Abstract

Estimation of the memory parameter in time series with long range dependence is considered. A pooled log periodogram regression estimator is proposed that utilizes a set of mL periodogram ordinates with L→∞ rather than m ordinates as in the conventional log periodogram estimator. Consistency and asymptotic normality of the pooled regression estimator are established. The pooled estimator is shown to have smaller asymptotic variance, but larger asymptotic bias, than the conventional log periodogram estimator. Finite sample performance is assessed in simulations and the methods are illustrated in an empirical application with inflation and stock returns.