Spectral analysis of unevenly spaced climatological time series

Spectral analysis is often based on the periodogram and on fitting a first-order autoregressive [AR(1)] process to data as climatological time series generally exhibit red noise spectra that can be well approximated by AR(1) models. When the periodogram exceeds some threshold at a frequency, the spectrum is said to differ from the AR(1) spectrum, and the frequency is generally taken as a member of the discrete spectrum. This traditional technique, however, must not be used without modifications for unevenly spaced data. Our purpose is to provide an AR(1) modeling tool that is more accurate than the TAUEST procedure commonly used for unevenly spaced paleoclimatical records. A periodogram based on an entire least square fit to unevenly spaced data is also introduced instead of the well-known Lomb-Scargle periodogram. The methodology is applied to two paleoclimatological records. Our results compared to those of a frequently used procedure (consisting of TAUEST and Lomb-Scargle periodogram) show some interesting differences.