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Monotone spectral density estimation. (English) Zbl 1209.62206

Summary: We propose two estimators of a monotone spectral density, that are based on the periodogram. These are the isotonic regression of the periodogram and the isotonic regression of the log-periodogram. We derive pointwise limit distribution results for the proposed estimators for short memory linear processes and long memory Gaussian processes and also that the estimators are rate optimal.

MSC:

62M15 Inference from stochastic processes and spectral analysis
62E20 Asymptotic distribution theory in statistics
62G08 Nonparametric regression and quantile regression
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62G07 Density estimation

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sapa; ftnonpar
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References:

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