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Empirical likelihood confidence regions in time series models. (English) Zbl 0882.62082

Summary: This paper develops empirical likelihood in time series models. By application of P. Whittle’s [Ark. Mat. 2, 423-434 (1953; Zbl 0053.41003)] estimation method, one obtains an \(M\)-estimator of the parameter of a stationary time series from approximately independent observations, the periodogram ordinates. This estimator is used to obtain an empirical likelihood ratio which is asymptotically distributed as \(\chi^2\) and which can be used to construct confidence regions. A procedure for the Bartlett correction is also proposed. Finally, small sample properties of the empirical likelihood confidence regions are explored through a simulation.

MSC:

62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62F25 Parametric tolerance and confidence regions

Citations:

Zbl 0053.41003
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