Efficient Bayesian PARCOR approaches for dynamic modeling of multivariate time series

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...

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Bibliographic Details
Published in:Journal of time series analysis 2020-11, Vol.41 (6), p.759-784
Main Authors: Zhao, Wenjie, Prado, Raquel
Format: Article
Language:English
Subjects:
Algorithms
Bayesian analysis
Bayesian dynamic linear models
Coherence
Computer simulation
Context
Dynamic models
Feasibility
Inference
Linear analysis
Multivariate analysis
Multivariate time series
Performance evaluation
Quality assessment
Representations
Simulation
Time measurement
Time series
Time-frequency analysis
time‐varying partial autocorrelations
time‐varying vector autoregressions
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Summary: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.
ISSN:0143-9782
1467-9892
DOI:10.1111/jtsa.12534