Time Varying Coefficient AR and VAR Models
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Autoregressive (AR) models are very useful for time series analysis. As shown in Figure 11.1, there is correspondence between the AR model and the autocovariance function and the power spectrum of an univariate stationary time series. Therefore, if an AR model is estimated from a time series, then the estimates of the autocovariance function and the power spectrum are obtained immediately. For the analysis of multivariate time series, Figure 11.2 shows the relation between the vector autoregressive (VAR) model and the cross-covariance function, the cross-spectrum, and the relative power contribution. Akaike and Nakagawa (1988), and Kitagawa (1993) developed procedures and programs for the analysis of stationary time series by using the AR and VAR models.
KeywordsKalman Filter State Space Representation Autocovariance Function Nonstationary Time Series Power Contribution
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