Multivariate time series analysis from a Bayesian machine learning perspective
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Multivariate time series analysis from a Bayesian machine learning perspective Jinwen Qiu1 · S. Rao Jammalamadaka1 · Ning Ning2
© Springer Nature Switzerland AG 2020
Abstract 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 datadriven 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. Keywords Multivariate analysis · Bayesian inference · Structural time series · Feature selection · Prediction Mathematics Subject Classification (2010) 62H86 · 62M10 · 62F15 · 62F07
1 Introduction A time series consists of a series of data points on the same variable(s) collected over time, and occurs frequently in statistics (see, for example, [3]), signal processing (see, for Ning Ning
[email protected] Jinwen Qiu [email protected] S. Rao Jammalamadaka [email protected] 1
Department of Statistics and Applied Probability, University of California, Santa Barbara, CA, USA
2
Department of Statistics, University of Michigan, Ann Arbor, MI, USA
J. Qiu et al.
example, [7]), pattern recognition (see, for example, [25]), econometrics (see, for example, [32]), mathematical finance (see, for example, [27]), control engineering (see, for example, [23]), to name a few. Time series analyses focus on extracting meaningful statistics and other characteristics of the data, with the primary goal of forecasting future values given previously observed values, which is extremely hard especially for multivariate target time series with a great number of contemporary explanatory variables. Nowadays, machine learning algorithms have become all pervasive and accomplished tasks that until recently only experts could perform. The world is gradually being reshaped by machines possessing “intelligence” and making our lives easier. Machine learning is encompassing every significant aspect of our lives and becoming an integral part of it. Applying machine learning techniques on time series forecast is very hard in general, mainly because common machine learning techniques assume sample independence, but the time series data do not qualify. While there is success in applying deep learning techniques on time series forecast in recent years (see, for example, [37]), theoretical support for d
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