Journal of Time Series Analysis

HIGHER ORDER MOMENTS OF SAMPLE AUTOCOVARIANCES AND SAMPLE AUTOCORRELATIONS FROM AN INDEPENDENT TIME SERIES

Journal Article

Abstract. Given length‐n sampled time series, generated by an independent distributed process, in this paper we treat the problem of determining the greatest order, in n, that moments of the sample autocovariances and sample autocorrelations can attain. For the sample autocovariance moments, we achieve quite general results; but, for the autocorrelation moments, we restrict study to Gaussian white noise (normal, independent and identically distributed). Our main theorem relates to the cross‐moments of the non‐centred sample autocovariances, but we also establish a relation between these and the corresponding moments for the centred sample autocovariances.

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