A Bayesian Curve Fitting Approach to Power Spectrum Estimation

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

doi:10.1080/10485250211389

Cited by 4 publications

(1 citation statement)

References 19 publications

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“…One can identify many previous contributions to Bayesian spectrum estimation, ranging from the classical work of Whittle () to contemporary Bayesian analyses including Mallick et al . (), Choudhuri et al . (), Pensky et al .…”

Section: Introductionmentioning

confidence: 96%

Should we Sample a time Series more Frequently?: Decision Support via Multirate Spectrum Estimation

Nason

Powell

Elliott

et al. 2016

Journal of the Royal Statistical Society Series A: Statistics in Society

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Summary. Suppose that we have a historical time series with samples taken at a slow rate, e.g. quarterly. The paper proposes a new method to answer the question: is it worth sampling the series at a faster rate, e.g. monthly? Our contention is that classical time series methods are designed to analyse a series at a single and given sampling rate with the consequence that analysts are not often encouraged to think carefully about what an appropriate sampling rate might be. To answer the sampling rate question we propose a novel Bayesian method that incorporates the historical series, cost information and small amounts of pilot data sampled at the faster rate. The heart of our method is a new Bayesian spectral estimation technique that is capable of coherently using data sampled at multiple rates and is demonstrated to have superior practical performance compared with alternatives. Additionally, we introduce a method for hindcasting historical data at the faster rate. A freeware R package, regspec, is available that implements our methods. We illustrate our work by using official statistics time series including the UK consumer price index and counts of UK residents travelling abroad, but our methods are general and apply to any situation where time series data are collected.

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Section: Introductionmentioning

confidence: 96%

Should we Sample a time Series more Frequently?: Decision Support via Multirate Spectrum Estimation

Nason

Powell

Elliott

et al. 2016

Journal of the Royal Statistical Society Series A: Statistics in Society

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Bayesian time series analysis of periodic behaviour and spectral structure

McCoy

Stephens

2004

International Journal of Forecasting

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A shrinkage estimator for spectral densities

Botts

Daniels

2006

Biometrika

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We propose a shrinkage estimator for spectral densities based on a multilevel normal hierarchical model. The first level captures the sampling variability via a likelihood constructed using the asymptotic properties of the periodogram. At the second level, the spectral density is shrunk towards a parametric time series model. To avoid selecting a particular parametric model for the second level, a third level is added which induces an estimator that averages over a class of parsimonious time series models. The estimator derived from this model, the model averaged shrinkage estimator, is consistent, is shown to be highly competitive with other spectral density estimators via simulations, and is computationally inexpensive.

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A Bayesian Curve Fitting Approach to Power Spectrum Estimation

Cited by 4 publications

References 19 publications

Should we Sample a time Series more Frequently?: Decision Support via Multirate Spectrum Estimation

Should we Sample a time Series more Frequently?: Decision Support via Multirate Spectrum Estimation

Bayesian time series analysis of periodic behaviour and spectral structure

A shrinkage estimator for spectral densities

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