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System identification using autoregressive Bayesian neural networks with nonparametric noise models

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  • Christos Merkatas
  • Simo Särkkä

Abstract

System identification is of special interest in science and engineering. This article is concerned with a system identification problem arising in stochastic dynamic systems, where the aim is to estimate the parameters of a system along with its unknown noise processes. In particular, we propose a Bayesian nonparametric approach for system identification in discrete time nonlinear random dynamical systems assuming only the order of the Markov process is known. The proposed method replaces the assumption of Gaussian distributed error components with a flexible family of probability density functions based on Bayesian nonparametric priors. Additionally, the functional form of the system is estimated by leveraging Bayesian neural networks, which leads to flexible uncertainty quantification. Hamiltonian Monte Carlo sampler within a Gibbs sampler for posterior inference is proposed and its effectiveness is illustrated in real time series.

Suggested Citation

  • Christos Merkatas & Simo Särkkä, 2023. "System identification using autoregressive Bayesian neural networks with nonparametric noise models," Journal of Time Series Analysis, Wiley Blackwell, vol. 44(3), pages 319-330, May.
  • Handle: RePEc:bla:jtsera:v:44:y:2023:i:3:p:319-330
    DOI: 10.1111/jtsa.12669
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    References listed on IDEAS

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    1. Chib, Siddhartha & Greenberg, Edward, 1994. "Bayes inference in regression models with ARMA (p, q) errors," Journal of Econometrics, Elsevier, vol. 64(1-2), pages 183-206.
    2. Carlos M. Carvalho & Nicholas G. Polson & James G. Scott, 2010. "The horseshoe estimator for sparse signals," Biometrika, Biometrika Trust, vol. 97(2), pages 465-480.
    3. Chib, Siddhartha & Greenberg, Edward, 2010. "Additive cubic spline regression with Dirichlet process mixture errors," Journal of Econometrics, Elsevier, vol. 156(2), pages 322-336, June.
    4. Juš Kocijan & Agathe Girard & Blaž Banko & Roderick Murray-Smith, 2005. "Dynamic systems identification with Gaussian processes," Mathematical and Computer Modelling of Dynamical Systems, Taylor & Francis Journals, vol. 11(4), pages 411-424, December.
    5. Albert, James H & Chib, Siddhartha, 1993. "Bayes Inference via Gibbs Sampling of Autoregressive Time Series Subject to Markov Mean and Variance Shifts," Journal of Business & Economic Statistics, American Statistical Association, vol. 11(1), pages 1-15, January.
    6. Fermanian, Adeline, 2021. "Embedding and learning with signatures," Computational Statistics & Data Analysis, Elsevier, vol. 157(C).
    7. Fuentes-García, Ruth & Mena, Ramsés H. & Walker, Stephen G., 2009. "A nonparametric dependent process for Bayesian regression," Statistics & Probability Letters, Elsevier, vol. 79(8), pages 1112-1119, April.
    8. Hatjispyros, Spyridon J. & Nicoleris, Theodoros & Walker, Stephen G., 2009. "A Bayesian nonparametric study of a dynamic nonlinear model," Computational Statistics & Data Analysis, Elsevier, vol. 53(12), pages 3948-3956, October.
    9. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
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