An Iterated Logarithm Result for Autocorrelations of a Stationary Linear Process

Abstract

Let $r(j)$ denote the $j$th autocorrelation based on a sample of $N$ consecutive observations on a stationary linear stochastic process. Under mild regularity conditions on the process, an iterated logarithm result is given for the convergence of $r(j)$ as $N \rightarrow \infty$ to the corresponding process autocorrelation $\rho (j)$.