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June 1996 Asymptotically optimal estimation in misspecified time series models
R. Dahlhaus, W. Wefelmeyer
Ann. Statist. 24(3): 952-974 (June 1996). DOI: 10.1214/aos/1032526951


A concept of asymptotically efficient estimation is presented when a misspecified parametric time series model is fitted to a stationary process. Efficiency of several minimum distance estimates is proved and the behavior of the Gaussian maximum likelihood estimate is studied. Furthermore, the behavior of estimates that minimize the h-step prediction error is discussed briefly. The paper answers to some extent the question what happens when a misspecified model is fitted to time series data and one acts as if the model were true.


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R. Dahlhaus. W. Wefelmeyer. "Asymptotically optimal estimation in misspecified time series models." Ann. Statist. 24 (3) 952 - 974, June 1996.


Published: June 1996
First available in Project Euclid: 20 September 2002

zbMATH: 0865.62063
MathSciNet: MR1401832
Digital Object Identifier: 10.1214/aos/1032526951

Primary: 62M10
Secondary: 62G20

Keywords: efficiency , maximum likelihood , minimum distance estimation , misspecified models , prediction , time series

Rights: Copyright © 1996 Institute of Mathematical Statistics

Vol.24 • No. 3 • June 1996
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