An Approximate Treatment of the Properties of the Correlogram and Periodogram

Summary M. G. Kendall (1946) has shown that the correlogram is unsatisfactory in that it has a characteristic undamped oscillation even when the generating auto-regressive relationship is highly damped, and that the periodogram is misleading in indicating spurious cyclical periods when applied to series generated by a known auto-regression relationship. This paper gives an approximate treatment of the problem designed to explain these features of the correlogram and periodogram. It is shown that the correlogram of an auto-regressive series can be regarded as though it were derived from an auto-regression equation of double the order of the equation generating the original series. Some properties of the periodograms of time series generated by linear stochastic equations are investigated, and the results are applied to the study of Beveridge’s wheat price index.