The Annals of Statistics

A likelihood approximation for locally stationary processes

Rainer Dahlhaus

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Abstract

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

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

Dates
First available in Project Euclid: 12 March 2002

Permanent link to this document
https://projecteuclid.org/euclid.aos/1015957480

Digital Object Identifier
doi:10.1214/aos/1015957480

Mathematical Reviews number (MathSciNet)
MR1835040

Zentralblatt MATH identifier
1010.62078

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

Keywords
Locally stationary Whittle likelihood local likelihood preperiodogram generalized Toeplitz matrices

Citation

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


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