A flexible two-piece normal dynamic linear model

We construct a flexible dynamic linear model for the analysis and prediction of multivariate time series, assuming a two-piece normal initial distribution for the state vector. We derive a novel Kalman filter for this model, obtaining a two components mixture as predictive and filtering distribution...

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Bibliographic Details
Published in:Computational statistics 2023-12, Vol.38 (4), p.2075-2096
Main Authors: Aliverti, Emanuele, Arellano-Valle, Reinaldo B., Kahrari, Fereshteh, Scarpa, Bruno
Format: Article
Language:English
Subjects:
Algorithms
Asymmetry
Bayesian analysis
Economic Theory/Quantitative Economics/Mathematical Methods
Kalman filters
Mathematics and Statistics
Normal distribution
Original Paper
Probability and Statistics in Computer Science
Probability Theory and Stochastic Processes
Random variables
Sequences
Skewness
State vectors
Statistical inference
Statistics
Time series
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Summary:We construct a flexible dynamic linear model for the analysis and prediction of multivariate time series, assuming a two-piece normal initial distribution for the state vector. We derive a novel Kalman filter for this model, obtaining a two components mixture as predictive and filtering distributions. In order to estimate the covariance of the error sequences, we develop a Gibbs-sampling algorithm to perform Bayesian inference. The proposed approach is validated and compared with a Gaussian dynamic linear model in simulations and on a real data set.
ISSN:0943-4062
1613-9658
DOI:10.1007/s00180-023-01355-3