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Autoregressive processes

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In this article, the definition, properties, and applications of linear autoregressive processes (or autoregressions) are reviewed. These form an important subset of the class of autoregressive moving‐average (ARMA) processes which are widely used as stationary models for time series data. Particular attention is paid to the problem of selecting and estimating appropriate autoregressions to describe empirically observed time series. WIREs Comp Stat 2011 3 316–331 DOI: 10.1002/wics.163

Figure 1.

Wolfer's annual sunspot numbers, 1749–1924.

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Figure 2.

The spectral density of Yule's autoregressive model for the sunspot series, 1749—1924, discussed in Example 3.

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Figure 3.

The autocorrelation function (left) and partial autocorrelation function (right) of Yule's model in Eq. (1) for the sunspot series, 1749–1924, plotted for lags 0–40 years.

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Figure 4.

The sample autocorrelation function (left) and sample partial autocorrelation function (right) for the annual sunspot numbers, 1749–1924.

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Figure 5.

The sample and model autocorrelation and partial autocorrelation functions for the annual sunspot numbers, 1749–1924, and the minimum AICC AR model.

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Figure 6.

The sample and model autocorrelation and partial autocorrelation functions for the for the annual sunspot numbers, 1749–1924, and the minimum AICC ARMA model.

[ Normal View | Magnified View ]

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Applications of Computational Statistics > Signal and Image Processing and Coding
Applications of Computational Statistics > Computational Mathematics
Data Structures > Time Series, Stochastic Processes, and Functional Data
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