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Autoregression quantiles and related rank-scores processes. (English) Zbl 0848.62047

Summary: This paper develops extensions of the regression quantiles of R. Koenker and G. Bassett [Econometrica 46, 33-50 (1978; Zbl 0373.62038)] to autoregression. It generalizes several results of J. Jurečková [A. K. Md. E. Saleh (ed.), Proc. Meeting Nonparam. Stat. Relat. Top., 217-228 (1992)] and C. Gutenbrunner and J. Jurečková [Ann. Stat. 20, No. 1, 305-330 (1992; Zbl 0759.62015)] in linear regression to autoregression models. In particular, it gives the asymptotic uniform linearity of linear rank-scores statistics based on residuals suitable in autoregression. It also discusses the two types of \(L\)-statistics appropriate in autoregression.

MSC:

62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62G20 Asymptotic properties of nonparametric inference
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