Smoothing Periodograms from Time-Series with Continuous Spectra

Abstract

IN his review¹ of M. G. Kendall‘s brochure² on oscillatory time-series, David G. Kendall made the pertinent observation that the smoothing of periodograms obtained from autoregressive or other time-series with continuous spectra is equivalent to considering the first few sample autocorrelations. I had arrived at a similar conclusion, though possibly by an alternative route, having noticed that the averaging of periodograms obtained from contiguous lengths of series is approximately equivalent to a truncation of the correlogram at a point represented by the length of the subseries. From preliminary computation already made on M. G. Kendall‘s artificial series to test out this smoothing device, it appears promising.