Monti, Anna Clara Empirical likelihood confidence regions in time series models. (English) Zbl 0882.62082 Biometrika 84, No. 2, 395-405 (1997). 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. Cited in 1 ReviewCited in 51 Documents MSC: 62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH) 62F25 Parametric tolerance and confidence regions Keywords:ARMA models; bootstrap; Whittle’s likelihood; empirical likelihood ratio Citations:Zbl 0053.41003 PDFBibTeX XMLCite \textit{A. C. Monti}, Biometrika 84, No. 2, 395--405 (1997; Zbl 0882.62082) Full Text: DOI