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AdaptSPEC: Adaptive Spectral Estimation for Nonstationary Time Series

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  • Ori Rosen
  • Sally Wood
  • David S. Stoffer

Abstract

We propose a method for analyzing possibly nonstationary time series by adaptively dividing the time series into an unknown but finite number of segments and estimating the corresponding local spectra by smoothing splines. The model is formulated in a Bayesian framework, and the estimation relies on reversible jump Markov chain Monte Carlo (RJMCMC) methods. For a given segmentation of the time series, the likelihood function is approximated via a product of local Whittle likelihoods. Thus, no parametric assumption is made about the process underlying the time series. The number and lengths of the segments are assumed unknown and may change from one MCMC iteration to another. The frequentist properties of the method are investigated by simulation, and applications to electroencephalogram and the El Niño Southern Oscillation phenomenon are described in detail.

Suggested Citation

  • Ori Rosen & Sally Wood & David S. Stoffer, 2012. "AdaptSPEC: Adaptive Spectral Estimation for Nonstationary Time Series," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(500), pages 1575-1589, December.
  • Handle: RePEc:taf:jnlasa:v:107:y:2012:i:500:p:1575-1589
    DOI: 10.1080/01621459.2012.716340
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    File URL: http://hdl.handle.net/10.1080/01621459.2012.716340
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    Cited by:

    1. Tommaso Proietti & Alessandra Luati, 2013. "The Exponential Model for the Spectrum of a Time Series: Extensions and Applications," CREATES Research Papers 2013-34, Department of Economics and Business Economics, Aarhus University.
    2. Zhang, Shibin, 2016. "Adaptive spectral estimation for nonstationary multivariate time series," Computational Statistics & Data Analysis, Elsevier, vol. 103(C), pages 330-349.

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