Estimation of Time Varying Variance
There are many time series whose structure involves a substantial change of variance. The decomposition of the seismic time series problem in Chapter 7 is such an example. In other practical data situations, the relatively fast wiggles of a nonstationary covariance time series appears to be modulated by a relatively slowly changing envelope function. For example, seismic measurements during an earthquake exhibit this behavior. That envelope function can be interpreted as a change of scale associated with the instantaneous innovations variance of the state space model of the time series. In this chapter the changing variance structure of the Urakawa-Oki, Hokkaido Japan March 21 1983, earthquake data, (code name MYN2F, Takanami 1991) is estimated by both Gaussian and non-Gaussian state space models. Additional applications include the change of variance modeling in the estimation of the log-periodogram of a time series and the estimation of the instantaneous variance of the collection of 21 years of daily maximum temperatures in Tokyo.
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