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Efficient Bayesian PARCOR approaches for dynamic modeling of multivariate time series

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  • Wenjie Zhao
  • Raquel Prado

Abstract

A Bayesian lattice filtering and smoothing approach is proposed for fast and accurate modeling and inference in multivariate non‐stationary time series. This approach offers computational feasibility and interpretable time‐frequency analysis in the multivariate context. The proposed framework allows us to obtain posterior estimates of the time‐varying spectral densities of individual time series components, as well as posterior measurements of the time‐frequency relationships across multiple components, such as time‐varying coherence and partial coherence. The proposed formulation considers multivariate dynamic linear models (MDLMs) on the forward and backward time‐varying partial autocorrelation coefficients (TV‐VPARCOR). Computationally expensive schemes for posterior inference on the multivariate dynamic PARCOR model are avoided using approximations in the MDLM context. Approximate inference on the corresponding time‐varying vector autoregressive (TV‐VAR) coefficients is obtained via Whittle's algorithm. A key aspect of the proposed TV‐VPARCOR representations is that they are of lower dimension, and therefore more efficient, than TV‐VAR representations. The performance of the TV‐VPARCOR models is illustrated in simulation studies and in the analysis of multivariate non‐stationary temporal data arising in neuroscience and environmental applications. Model performance is evaluated using goodness‐of‐fit measurements in the time‐frequency domain and also by assessing the quality of short‐term forecasting.

Suggested Citation

  • Wenjie Zhao & Raquel Prado, 2020. "Efficient Bayesian PARCOR approaches for dynamic modeling of multivariate time series," Journal of Time Series Analysis, Wiley Blackwell, vol. 41(6), pages 759-784, November.
  • Handle: RePEc:bla:jtsera:v:41:y:2020:i:6:p:759-784
    DOI: 10.1111/jtsa.12534
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    1. Raquel Prado & Mike West & Andrew D. Krystal, 2001. "Multichannel electroencephalographic analyses via dynamic regression models with time‐varying lag–lead structure," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 50(1), pages 95-109.
    2. Christoph Schmidt & Britta Pester & Nicole Schmid-Hertel & Herbert Witte & Axel Wismüller & Lutz Leistritz, 2016. "A Multivariate Granger Causality Concept towards Full Brain Functional Connectivity," PLOS ONE, Public Library of Science, vol. 11(4), pages 1-25, April.
    3. Zhe Yu & Raquel Prado & Erin Burke Quinlan & Steven C. Cramer & Hernando Ombao, 2016. "Understanding the Impact of Stroke on Brain Motor Function: A Hierarchical Bayesian Approach," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(514), pages 549-563, April.
    4. Guofu Zhou, 1992. "Algorithms For Estimation Of Possibly Nonstationary Vector Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 13(2), pages 171-188, March.
    5. 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.
    6. Annalisa Cadonna & Athanasios Kottas & Raquel Prado, 2019. "Bayesian Spectral Modeling for Multiple Time Series," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 114(528), pages 1838-1853, October.
    7. K. Triantafyllopoulos, 2007. "Covariance estimation for multivariate conditionally Gaussian dynamic linear models," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 26(8), pages 551-569.
    8. Scott A. Bruce & Martica H. Hall & Daniel J. Buysse & Robert T. Krafty, 2018. "Conditional adaptive Bayesian spectral analysis of nonstationary biomedical time series," Biometrics, The International Biometric Society, vol. 74(1), pages 260-269, March.
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    1. Sui, Yuelei & Holan, Scott H. & Yang, Wen-Hsi, 2023. "Bayesian circular lattice filters for computationally efficient estimation of multivariate time-varying autoregressive models," Computational Statistics & Data Analysis, Elsevier, vol. 181(C).

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