Self-Affine Time Series: I. Generation and Analyses

Abstract

This chapter introduces the basic concepts of self-affine time series. In a self-affine time series, the power-spectral density is defined as a power-law function of the frequency. Time series are quantified by their statistical distribution of values and by their persistence or antipersistence. Persistence can be classified in terms of range, short-range or long-range, and in terms of strength, weak, or strong. The distribution of values is usually either Gaussian (normal) or log-normal. The basic characteristic of a self-affine time series is that the persistence is scale invariant. Thus, a self-affine time series has a long-range persistence and these are found in a wide variety of geophysical applications. The chapter examines a variety of techniques to quantify the strength of long-range persistence in self-affine time series. These include Fourier power-spectral analysis, semivariogram analysis, rescaled-range analysis, average extreme-event analysis, and wavelet variance analysis.

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