The second-order moments of the sample covariances for time series with missing observations

The estimation of the covariances of a stationary time series with missing observations is considered. General formulas for the asymptotic second-order moments of the sample covariances of such a time series are given for either random or deterministic patterns of misses. Closed-form expressions are derived for the random Bernoulli pattern and for the deterministic periodic pattern of missing observations and are explicitly evaluated for autoregressive moving-average time series. These results are useful for constructing and analyzing parameter or spectrum estimation algorithms based on the sample covariances for a stationary time series with missing observations