Estimation of spectral density of a stationary time series via an asymptotic representation of the periodogram

Gangopadhyay, Ashis; Mallick, Bani K.; Denison, D. G. T.

doi:10.1016/s0378-3758(98)00148-7

Cited by 19 publications

(19 citation statements)

References 8 publications

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“…However, there the aim is usually to produce consistent and smooth estimates of the spectrum, and the approaches applied include e.g. averaging [55,32], smoothing via splines [56] or Bayesian model fitting [57,58]. The approach to modelling the noise spectrum introduced here is different in that the spectrum per se is not of interest, or only of interest as far as it enters into likelihood computations.…”

Section: Discussionmentioning

confidence: 99%

Modelling coloured residual noise in gravitational-wave signal processing

Röver

Meyer

Christensen

2010

Class. Quantum Grav.

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Abstract. We introduce a signal processing model for signals in non-white noise, where the exact noise spectrum is a priori unknown. The model is based on a Student's t distribution and constitutes a natural generalization of the widely used normal (Gaussian) model. This way, it allows for uncertainty in the noise spectrum, or more generally is also able to accommodate outliers (heavy-tailed noise) in the data. Examples are given pertaining to data from gravitational wave detectors.

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Section: Discussionmentioning

confidence: 99%

Modelling coloured residual noise in gravitational-wave signal processing

Röver

Meyer

Christensen

2010

Class. Quantum Grav.

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“…Ombao, Raz, Strawderman, and von Sachs (2001) described a Whittle likelihood-based generalized cross-validation method for selecting the bandwidth in periodogram smoothing. Nonparametric Bayesian approaches to the estimation of a spectral density were studied by Carter and Kohn (1997), Gangopadhyay, Mallick, andDenison (1998), andLiseo, Marinucci, andPetrella (2001), who used the Whittle likelihood to obtain a pseudoposterior distribution of f * . Carter and Kohn (1997) induced a prior on the logarithm of f * through an integrated Wiener process and provided elegant computational methods for computing the posterior.…”

Section: Introductionmentioning

confidence: 99%

“…Liseo et al (2001) considered a Brownian motion for the spectral density and modified it around the zero frequency to incorporate the long-range dependence. Gangopadhyay et al (1998) fitted piecewise polynomials of a fixed low order to the logarithm of f * while putting priors on the number of knots, the location of the knots, and the coefficients of the polynomials. Although these methods were applied to some real and simulated data, their theoretical properties are unknown.…”

Section: Introductionmentioning

confidence: 99%

Bayesian Estimation of the Spectral Density of a Time Series

Choudhuri

Ghosal

Roy

2004

Journal of the American Statistical Association

110

182

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This article describes a Bayesian approach to estimating the spectral density of a stationary time series. A nonparametric prior on the spectral density is described through Bernstein polynomials. Because the actual likelihood is very complicated, a pseudoposterior distribution is obtained by updating the prior using the Whittle likelihood. A Markov chain Monte Carlo algorithm for sampling from this posterior distribution is described that is used for computing the posterior mean, variance, and other statistics. A consistency result is established for this pseudoposterior distribution that holds for a short-memory Gaussian time series and under some conditions on the prior. To prove this asymptotic result, a general consistency theorem of Schwartz is extended for a triangular array of independent, nonidentically distributed observations. This extension is also of independent interest. A simulation study is conducted to compare the proposed method with some existing methods. The method is illustrated with the well-studied sunspot dataset.

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“…Given g, the conditional posterior distribution of the latent variables are independent and samples are easily drawn from their finite support. Gangopadhyay et al (1998) considered the free-not spline approach to modeling g. In this case, the posterior is computed by the reversible jump algorithm of Green (1995). Liseo et al (2001) considered a Brownian motion process as prior on g. For sampling from the posterior distribution, they considered the Karhunen-Loévé series expansion for the Brownian motion and then truncated the infinite series to a finite sum.…”

Section: Gaussian Process Priormentioning

confidence: 99%