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Multivariate time series analysis from a Bayesian machine learning perspective. (English) Zbl 07342710
Summary: In this paper, we perform multivariate time series analysis from a Bayesian machine learning perspective through the proposed multivariate Bayesian time series (MBTS) model. The multivariate structure and the Bayesian framework allow the model to take advantage of the association structure among target series, select important features, and train the data-driven model at the same time. Extensive analyses on both simulated data and empirical data indicate that the MBTS model is able to, cover the true values of regression coefficients in $$90\%$$ credible intervals, select the most important predictors, and boost the prediction accuracy with higher correlation in absolute value of the target series, and consistently yield superior performance over the univariate Bayesian structural time series (BSTS) model, the autoregressive integrated moving average with regression (ARIMAX) model, and the multivariate ARIMAX (MARIMAX) model, in one-step-ahead forecast and ten-steps-ahead forecast.
##### MSC:
 62H12 Estimation in multivariate analysis 62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH) 62F15 Bayesian inference 62F07 Statistical ranking and selection procedures 68T05 Learning and adaptive systems in artificial intelligence
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