Sankhya: The Indian Journal of Statistics

1999, Volume 61, Series A, Pt. 2, 189-207

ESTIMATION OF THE AUTOCORRELATION FUNCTION OF A STATIONARY TIME SERIES WITH MISSING OBSERVATIONS

By

YOSHIHIRO YAJIMA, University of Tokyo, Bunkyo

and

HARUHISA NISHINO, Tokyo Metropolitan University, Hachiouji

SUMMARY. We consider three estimators of the autocorrelation function for a stationary process with missing observations. The first estimator is linked with the Yule-Walker estimator, the second one the least squares estimator, and the third one the sample correlation coefficient. We clarify their asymptotic differences and derive asymptotic distributions for both short-memory and long-memory models. In most of short-memory models the third estimator has a smaller asymptotic variance than the others. On the other hand, if a process follows a long-memory model and its spectral density function is not square integrable, then the asymptotic distributions of the three estimators are all the same and, moreover, are still the same as those of estimators under complete sampling too.

AMS (1991) subject classification. 62M10, 90A20.

Key words and phrases. Autocorrelation, missing observations, long-memory time series.

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