Estimation of Time Varying Variance

  • Genshiro Kitagawa
  • Will Gersch
Part of the Lecture Notes in Statistics book series (LNS, volume 116)


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.


State Space Model Trend Model Time Vary Variance Variance Time Series Instantaneous Variance 
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Copyright information

© Springer Science+Business Media New York 1996

Authors and Affiliations

  • Genshiro Kitagawa
    • 1
  • Will Gersch
    • 2
  1. 1.The Institute of Statistical MathematicsTokyoJapan
  2. 2.Department of Information and Computer ScienceUniversity of HawaiiHonoluluUSA

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