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Abstract In this article the definition, properties, and applications of the autocovariance function of a stationary time series are reviewed. Particular attention is given to univariate and multivariate stationary sequences and to univariate continuous‐time stationary processes. Numerous illustrative examples are given. Copyright © 2009 John Wiley & Sons, Inc. This article is categorized under: Data: Types and Structure > Time Series, Stochastic Processes, and Functional Data

The sample autocorrelation function of a sample of size 200 from a Gaussian IID(0,1) series, showing the bounds (Example 8).

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The sample correlations for the bivariate series shown in Figure 2 and discussed in Example 9.

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Percentage daily log returns on the Dow‐Jones Industrial Index (Series 1) and the Australian All‐ordinaries Index for 250 consecutive trading days up to 26 August 1994.

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Data: Types and Structure > Time Series, Stochastic Processes, and Functional Data

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