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Sparse vector Markov switching autoregressive models. Application to multivariate time series of temperature

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  • Monbet, Valérie
  • Ailliot, Pierre

Abstract

Multivariate time series are of interest in many fields including economics and environment. The dynamical processes occurring in these domains often exhibit a mixture of different dynamics so that it is common to describe them using Markov Switching vector autoregressive processes. However the estimation of such models is difficult even when the dimension is not so high because of the number of parameters involved. A Smoothly Clipped Absolute Deviation penalization of the likelihood is proposed to shrink the parameters towards zeros and regularize the inference problem which is generally ill-posed. The Expectation Maximization algorithm built for maximizing the penalized likelihood is described in detail and tested on simulated data and real data consisting of daily mean temperature.

Suggested Citation

  • Monbet, Valérie & Ailliot, Pierre, 2017. "Sparse vector Markov switching autoregressive models. Application to multivariate time series of temperature," Computational Statistics & Data Analysis, Elsevier, vol. 108(C), pages 40-51.
    • Handle: RePEc:eee:csdana:v:108:y:2017:i:c:p:40-51
    DOI: 10.1016/j.csda.2016.10.023
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    References listed on IDEAS

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    1. Luigi Spezia & Andy Vinten & Roberta Paroli & Marc Stutter, 2021. "An evolutionary Monte Carlo method for the analysis of turbidity high‐frequency time series through Markov switching autoregressive models," Environmetrics, John Wiley & Sons, Ltd., vol. 32(8), December.
    2. Oscar V. De la Torre-Torres & Evaristo Galeana-Figueroa & José Álvarez-García, 2019. "A Test of Using Markov-Switching GARCH Models in Oil and Natural Gas Trading," Energies, MDPI, vol. 13(1), pages 1-24, December.
    3. Yuan Yan & Hsin-Cheng Huang & Marc G. Genton, 2021. "Vector Autoregressive Models with Spatially Structured Coefficients for Time Series on a Spatial Grid," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 26(3), pages 387-408, September.
    4. Spezia, Luigi, 2020. "Bayesian variable selection in non-homogeneous hidden Markov models through an evolutionary Monte Carlo method," Computational Statistics & Data Analysis, Elsevier, vol. 143(C).
    5. Kenwin Maung, 2021. "Estimating high-dimensional Markov-switching VARs," Papers 2107.12552, arXiv.org.
    6. Nina Kargapolova, 2021. "Numerical Stochastic Model of Non-stationary Time Series of the Wind Chill Index," Methodology and Computing in Applied Probability, Springer, vol. 23(1), pages 257-271, March.

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