Estimation for almost periodic processes. (English) Zbl 1113.62111

Lii, Keh-Shin; Rosenblatt, Murray

Ann. Stat. 34, No. 3, 1115-1139 (2006).

Summary: Processes with almost periodic covariance functions have spectral mass on lines parallel to the diagonal in the two-dimensional spectral plane. Methods have been given for estimation of spectral mass on the lines of spectral concentration if the locations of the lines are known. Here methods for estimating the intercepts of the lines of spectral concentration in the Gaussian case are given under appropriate conditions. The methods determine rates of convergence sufficiently fast as the sample size \(n\to\infty\) so that the spectral estimation on the estimated lines can then proceed effectively. This task involves bounding the maximum of an interesting class of non-Gaussian possibly nonstationary processes.

MSC:

62M15	Inference from stochastic processes and spectral analysis
62G05	Nonparametric estimation
62M10	Time series, auto-correlation, regression, etc. in statistics (GARCH)
62M99	Inference from stochastic processes

Keywords:

almost periodic covariance; spectral estimation; periodogram; process maximum; Gaussian and non-Gaussian process; frequency detection and estimation

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