Topic
Spectral density estimation
About: Spectral density estimation is a research topic. Over the lifetime, 5391 publications have been published within this topic receiving 123105 citations.
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TL;DR: The estimates are shown to be consistent under mild smoothness conditions on the spectral density and it is shown that the periodograms of the two classes have distinct statistics.
Abstract: A class of spectral estimates of continuous-time stationary stochastic processes X(t) from a finite number of observations \{X(t_{n})\}^{N}_{n}=l taken at Poisson sampling instants \{t_{n}\} is considered. The asymptotic bias and covariance of the estimates are derived, and the influence of the spectral windows and the sampling rate on the performance of the estimates is discussed. The estimates are shown to be consistent under mild smoothness conditions on the spectral density. Comparison is made with a related class of spectral estimates suggested in [15] where the number of observations is {\em random}. It is shown that the periodograms of the two classes have distinct statistics.
100 citations
TL;DR: This paper presents approximations which allow an efficient computation and compensation of the bias in moving average and first-order recursive smoothed psd estimates and discusses factors that influence the bias.
100 citations
TL;DR: In this paper, the authors consider nonparametric estimation of spectral densities of stationary processes, and obtain consistency and asymptotic normality of spectral density estimates under natural and easily verifiable conditions.
Abstract: We consider nonparametric estimation of spectral densities of stationary processes, a fundamental problem in spectral analysis of time series. Under natural and easily verifiable conditions, we obtain consistency and asymptotic normality of spectral density estimates. Asymptotic distribution of maximum deviations of the spectral density estimates is also derived. The latter result sheds new light on the classical problem of tests of white noises.
99 citations
TL;DR: In this paper, the authors developed the basic building blocks of a frequency domain framework for drawing statistical inferences on the second-order structure of a stationary sequence of functional data, and derived an asymptotic Gaussian representation of the fDFT, thus allowing the transformation of the original collection of dependent random functions into a collection of approximately independent complexvalued Gaussian random functions.
Abstract: We develop the basic building blocks of a frequency domain framework for drawing statistical inferences on the second-order structure of a stationary sequence of functional data. The key element in such a context is the spectral density operator, which generalises the notion of a spectral density matrix to the functional setting, and characterises the second-order dynamics of the process. Our main tool is the functional Discrete Fourier Transform (fDFT). We derive an asymptotic Gaussian representation of the fDFT, thus allowing the transformation of the original collection of dependent random functions into a collection of approximately independent complex-valued Gaussian random functions. Our results are then employed in order to construct estimators of the spectral density operator based on smoothed versions of the periodogram kernel, the functional generalisation of the periodogram matrix. The consistency and asymptotic law of these estimators are studied in detail. As immediate consequences, we obtain central limit theorems for the mean and the long-run covariance operator of a stationary functional time series. Our results do not depend on structural modelling assumptions, but only functional versions of classical cumulant mixing conditions, and are shown to be stable under discrete observation of the individual curves.
98 citations
TL;DR: In this paper, the authors make use of a matched filter bank (MAFI) approach to derive spectral estimators for stationary signals with mixed spectra, and they show that the Capon spectral estimator as well as the more recently recently proposed CCA estimator can be computed using the same approach.
98 citations