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Adaptive spectral estimation for nonstationary multivariate time series

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  • Zhang, Shibin

Abstract

Following the nonstationary univariate time series model of Rosen et al. (2012), we propose an adaptive estimation of time-varying spectra and cross-spectra for analyzing possibly nonstationary multivariate time series. Under the Bayesian framework, the estimation is implemented by smoothing stochastic approximation Monte Carlo (SSAMC) methods. We show by simulation study that the proposed method achieves good performance for time series whether changing abruptly or smoothly. The superiority to the other existing methods is also investigated. An application to longitudinal vibration data of the containership provides a wave-approach angle range, which should be recommended when sailing under a harsh sea condition.

Suggested Citation

  • Zhang, Shibin, 2016. "Adaptive spectral estimation for nonstationary multivariate time series," Computational Statistics & Data Analysis, Elsevier, vol. 103(C), pages 330-349.
    • Handle: RePEc:eee:csdana:v:103:y:2016:i:c:p:330-349
    DOI: 10.1016/j.csda.2016.05.025
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    References listed on IDEAS

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    1. Ori Rosen & David S. Stoffer, 2007. "Automatic estimation of multivariate spectra via smoothing splines," Biometrika, Biometrika Trust, vol. 94(2), pages 335-345.
    2. Guo, Wensheng & Dai, Ming & Ombao, Hernando C. & von Sachs, Rainer, 2003. "Smoothing Spline ANOVA for Time-Dependent Spectral Analysis," Journal of the American Statistical Association, American Statistical Association, vol. 98, pages 643-652, January.
    3. Beran, Jan & Heiler, Mark A., 2008. "A nonparametric regression cross spectrum for multivariate time series," Journal of Multivariate Analysis, Elsevier, vol. 99(4), pages 684-714, April.
    4. Beran, Jan, 2008. "A nonparametric regression cross spectrum for multivariate time series," CoFE Discussion Papers 08/01, University of Konstanz, Center of Finance and Econometrics (CoFE).
    5. Liang, Faming & Liu, Chuanhai & Carroll, Raymond J., 2007. "Stochastic Approximation in Monte Carlo Computation," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 305-320, March.
    6. Davis, Richard A. & Lee, Thomas C.M. & Rodriguez-Yam, Gabriel A., 2006. "Structural Break Estimation for Nonstationary Time Series Models," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 223-239, March.
    7. Sally A. Wood, 2002. "Bayesian mixture of splines for spatially adaptive nonparametric regression," Biometrika, Biometrika Trust, vol. 89(3), pages 513-528, August.
    8. Rosen, Ori & Stoffer, David S. & Wood, Sally, 2009. "Local Spectral Analysis via a Bayesian Mixture of Smoothing Splines," Journal of the American Statistical Association, American Statistical Association, vol. 104(485), pages 249-262.
    9. Ombao H. C & Raz J. A & von Sachs R. & Malow B. A, 2001. "Automatic Statistical Analysis of Bivariate Nonstationary Time Series," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 543-560, June.
    10. Ombao, Hernando & von Sachs, Rainer & Guo, Wensheng, 2005. "SLEX Analysis of Multivariate Nonstationary Time Series," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 519-531, June.
    11. Ming Dai, 2004. "Multivariate spectral analysis using Cholesky decomposition," Biometrika, Biometrika Trust, vol. 91(3), pages 629-643, September.
    12. Robert T. Krafty & William O. Collinge, 2013. "Penalized multivariate Whittle likelihood for power spectrum estimation," Biometrika, Biometrika Trust, vol. 100(2), pages 447-458.
    13. 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.
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    Cited by:

    1. Hu, Zhixiong & Prado, Raquel, 2023. "Fast Bayesian inference on spectral analysis of multivariate stationary time series," Computational Statistics & Data Analysis, Elsevier, vol. 178(C).
    2. Zhang, Shibin, 2019. "Bayesian copula spectral analysis for stationary time series," Computational Statistics & Data Analysis, Elsevier, vol. 133(C), pages 166-179.
    3. Chau, Joris & von Sachs, Rainer, 2022. "Time-varying spectral matrix estimation via intrinsic wavelet regression for surfaces of Hermitian positive definite matrices," Computational Statistics & Data Analysis, Elsevier, vol. 174(C).
    4. Meier, Alexander & Kirch, Claudia & Meyer, Renate, 2020. "Bayesian nonparametric analysis of multivariate time series: A matrix Gamma Process approach," Journal of Multivariate Analysis, Elsevier, vol. 175(C).
    5. Chau, Van Vinh & von Sachs, Rainer, 2018. "Intrinsic wavelet regression for surfaces of Hermitian positive definite matrices," LIDAM Discussion Papers ISBA 2018025, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    6. Shibin Zhang, 2022. "Automatic estimation of spatial spectra via smoothing splines," Computational Statistics, Springer, vol. 37(2), pages 565-590, April.
    7. Zhang, Shibin, 2020. "Nonparametric Bayesian inference for the spectral density based on irregularly spaced data," Computational Statistics & Data Analysis, Elsevier, vol. 151(C).

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