Statistical and spectral properties of some paleomagnetic/paleoclimatic time series

Abstract

Power spectra were computed for the six paleomagnetic records in Wollin et al. (1977) and for composite time series formed by adding the six records sequentially. Use of the composite series reduces the noise associated with local magnetic and climatic variability. The statistical properties of the composite were found to be insensitive to the ordering of the individual records. Maximum likelihood estimates for the theoretical autocorrelation function of the composite data spaced at intervals of 10,000 years show that the data are described by a second order autoregressive process with first and second order coefficients 0.7 and −0.2. The theoretical power spectrum for these coefficients is monotonically increasing with period becoming nearly flat at periods longer than 100,000 years. Spectra with lag windows of 25 and 50 do not have peaks exceeding the 95% confidence limits. A 100 lag window spectrum has peaks exceeding the confidence limits at 105, 7.4×104 and 2.16×104 yr; however, since it is quite common for artificial paleomagnetic time series generated from the above second order autoregressive process to have significant peaks near one or more of the Earth's three orbital frequencies when using a 100 lag window, one must conclude that there is little if any reliable evidence for orbital forcing in the data studied.