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Rate of convergence for logspline spectral density estimation. (English) Zbl 0832.62082
Summary: The logarithm of the spectral density function for a stationary process is approximated by polynomial splines. The approximation is chosen to maximize the expected log-likelihood based on the asymptotic properties of the periodogram. Estimates of this approximation are shown to possess the usual nonparametric rate of convergence when the number of knots suitably increases to infinity.

MSC:
62M15 Inference from stochastic processes and spectral analysis
62G20 Asymptotic properties of nonparametric inference
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
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