The Annals of Statistics

Asymptotically optimal estimation in misspecified time series models

R. Dahlhaus and W. Wefelmeyer

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Abstract

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

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

Dates
First available in Project Euclid: 20 September 2002

Permanent link to this document
https://projecteuclid.org/euclid.aos/1032526951

Digital Object Identifier
doi:10.1214/aos/1032526951

Mathematical Reviews number (MathSciNet)
MR1401832

Zentralblatt MATH identifier
0865.62063

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

Keywords
Time series misspecified models efficiency minimum distance estimation maximum likelihood prediction

Citation

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. https://projecteuclid.org/euclid.aos/1032526951


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