Time Series Analysis of Holocene Climate Data
Abstract
Holocene climate records are imperfect proxies for processes containing complicated mixtures of periodic and random signals. I summarize time series analysis methods for such data with emphasis on the multipledatawindow technique. This method differs from conventional approaches to time series analysis in that a set of data tapers is applied to the data in the time domain before Fourier transforming. The tapers, or data windows, are discrete prolate spheroidal sequences characterized as being the most nearly bandlimited functions possible among functions defined on a finite time domain. The multiplewindow method is a smallsample theory and essentially an inverse method applied to the finite Fourier transform. For climate data it has the major advantage of providing a narrowband Ftest for the presence and significance of periodic components and of being able to separate them from the nondeterministic part of the process. Confidence intervals for the estimated quantities are found by jackknifing across windows. Applied to ^{14}C records, this method confirms the presence of the `Suess wiggles' and give an estimated period of 208.2 years. Analysis of the thickness variations of bristlecone pine growth rings shows a general absence of direct periodic components but a variation in the structure of the time series with a 2360year period.
 Publication:

Philosophical Transactions of the Royal Society of London Series A
 Pub Date:
 April 1990
 DOI:
 10.1098/rsta.1990.0041
 Bibcode:
 1990RSPTA.330..601T