Time Series Analysis of Holocene Climate Data

Holocene climate records are imperfect proxies for processes containing complicated mixtures of periodic and random signals. We summarize interpolation and time-series analysis methods for such data with emphasis on multiple-window techniques. This method (Proc. IEEE 70, pp 1055-96, 1982) differs from conventional approaches in that a set of data tapers is applied to the data before Fourier transforming. The tapers, or data windows, are discrete prolate spheroidal sequences (Bell System Tech. J. 57, pp 1371-1430, 1978) characterized as being the most nearly bandlimited functions possible among functions defined on a finite time domain. It is a small sample theory and essentially an inverse method applied to the finite Fourier transform. For climate data it has the major advantages of providing a narrowband F test for the presence of periodic components and of being able to separate them from the non-deterministic part of the process. Confidence intervals for the estimated quantities are found by jackknifing across windows.