COWLES FOUNDATION FOR RESEARCH IN ECONOMICS
AT YALE UNIVERSITY

Box 208281
New Haven, CT 06520-8281

COWLES FOUNDATION DISCUSSION PAPER NO. 1267

Pooled Log Periodogram Regression

Katsumi Shimotsu and Peter C.B. Phillips

July 2000

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 approaching infinity rather than m ordinates used 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 variance but larger 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.

Keywords: Discrete Fourier transform, log periodogram regression, long memory parameter, pooling frequency bands, semiparametric estimation

JEL Classification: C22