THE EXACT BIAS OF THE LOG-PERIODOGRAM REGRESSION ESTIMATOR

Abstract

The paper makes two contributions. First, we provide a formula for the exact distribution of the periodogram evaluated at any arbitrary frequency, when the sample is taken from any zero-mean stationary Gaussian process. The inadequacy of the asymptotic distribution is demonstrated through an example in which the observations are generated by a fractional Gaussian noise process. The results are then applied in deriving the exact bias of the log-periodogram regression estimator (Geweke and Porter-Hudak (1983), Robinson (1995)). The formula is computable. Practical bounds on this bias are developed and their arithmetic mean is shown to be accurate and useful.

Keywords:

• ARFIMA
• Chi-square distribution
• Log-periodogram regression

ACKNOWLEDGMENTS

Thanks are due to Arkadi Nemirovski, an associate editor and a referee for many helpful comments.