The Annals of Statistics

A likelihood approximation for locally stationary processes

Rainer Dahlhaus

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A new approximation to the Gaussian likelihood of a multivariate locally stationary process is introduced. It is based on an approximation of the inverse of the covariance matrix of such processes. The new quasi likelihood is a generalization of the classical Whittle likelihood for stationary processes. Several approximation results are proved for the likelihood function. For parametric models, asymptotic normality and efficiency of the resulting estimator are derived for Gaussian locally stationary processes.

Article information

Ann. Statist., Volume 28, Number 6 (2000), 1762-1794.

First available in Project Euclid: 12 March 2002

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62M10: Time series, auto-correlation, regression, etc. [See also 91B84]
Secondary: 62F10: Point estimation

Locally stationary Whittle likelihood local likelihood preperiodogram generalized Toeplitz matrices


Dahlhaus, Rainer. A likelihood approximation for locally stationary processes. Ann. Statist. 28 (2000), no. 6, 1762--1794. doi:10.1214/aos/1015957480.

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