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Oracally efficient estimation of autoregressive error distribution with simultaneous confidence band. (English) Zbl 1308.62096

The authors consider estimation for the cumulative distribution function of unobserved errors in autoregressive time series. Two estimates of the cdf \(F(z)\) are considered: a kernel distribution estimator \(\widehat{F}(z)\) and a two-step plug-in estimator \(\widehat{F}(z)\). The uniform closeness of these estimates under Hölder continuity assumption on \(F\) is proved in Section 2. In Sections 3 and 4, implementation and performance of the estimators are discussed. Performance results are presented for the standard normal distribution and standard double exponential distribution.

MSC:

62G15 Nonparametric tolerance and confidence regions
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
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References:

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