Miscellaneous Applications

Abstract

A method of last resort, when more sophisticated methods are not tractable or not available, is the method of moments, which typically relies on an ergodic theorem and involves no significant structural assumptions. Nevertheless, in various circumstances, such as for estimating the mean of a stationary process, it turns out that the method of moments (which estimates EX _i = θ by $T^{ - 1} \sum _{i = 1}^T X_i$ produces an estimator that has the same asymptotic variance as the best linear unbiased estimator (BLUE) under broad conditions on the spectral density or covariance function. This is of considerable practical significance. The discussion in this section follows the papers Heyde (1988b), (1992b).