The Annals of Statistics

Asymptotically optimal estimation in misspecified time series models

R. Dahlhaus and W. Wefelmeyer

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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.

Article information

Ann. Statist., Volume 24, Number 3 (1996), 952-974.

First available in Project Euclid: 20 September 2002

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62M10: Time series, auto-correlation, regression, etc. [See also 91B84]
Secondary: 62G20: Asymptotic properties

Time series misspecified models efficiency minimum distance estimation maximum likelihood prediction


Dahlhaus, R.; Wefelmeyer, W. Asymptotically optimal estimation in misspecified time series models. Ann. Statist. 24 (1996), no. 3, 952--974. doi:10.1214/aos/1032526951.

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