The Annals of Statistics

Fitting time series models to nonstationary processes

R. Dahlhaus

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A general minimum distance estimation procedure is presented for nonstationary time series models that have an evolutionary spectral representation. The asymptotic properties of the estimate are derived under the assumption of possible model misspecification. For autoregressive processes with time varying coefficients, the estimate is compared to the least squares estimate. Furthermore, the behavior of estimates is explained when a stationary model is fitted to a nonstationary process.

Article information

Ann. Statist. Volume 25, Number 1 (1997), 1-37.

First available: 10 October 2002

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Mathematical Reviews number (MathSciNet)

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Zentralblatt MATH identifier

Primary: 62M15: Spectral analysis
Secondary: 62F10: Point estimation

Nonstationary processes time series evolutionary spectra minimum distance estimates model selection


Dahlhaus, R. Fitting time series models to nonstationary processes. The Annals of Statistics 25 (1997), no. 1, 1--37. doi:10.1214/aos/1034276620.

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