6. Time (or Space) Series Analysis

In this chapter we will consider some common aspects of time series analysis including autocorrelation, statistical prediction, harmonic analysis, power spectrum analysis, and cross-spectrum analysis. We will also consider space-time cross spectral analysis, a combination of time-Fourier and space-Fourier analysis, which is often used in meteorology. The techniques of time series analysis described here are frequently encountered in all of geoscience and in many other fields. We will spend most of our time on classical Fourier spectral analysis, but will mention briefly other approaches such as Maximum Entropy (MEM), Singular Spectrum Analysis (SSA) and the Multi-Taper Method (MTM). Although we include a discussion of the historical Lag-correlation spectral analysis method, we will focus primarily on the Fast Fourier Transform (FFT) approach. First a few basic