The Uniform Convergence of Autocovariances

The Annals of Statistics · 1974 · Volume 2 · Issue 4

Abstract

Under general circumstances it is shown that the sample autocovariances of a discrete, stationary, ergodic process with finite covariance which is also purely nondeterministic converge, uniformly on the lag, almost surely to the true values. The result is used to prove the almost sure convergence, uniform in a parameter, of an expression relevant to the estimation of a lagged relation between two series.

Keywords

60G10, 62M10, Almost sure convergence, autocovariance, group delay, stationary process

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