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A Class of Non-Gaussian State Space Models With Exact Likelihood Inference

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  • Drew D. Creal

Abstract

The likelihood function of a general nonlinear, non-Gaussian state space model is a high-dimensional integral with no closed-form solution. In this article, I show how to calculate the likelihood function exactly for a large class of non-Gaussian state space models that include stochastic intensity, stochastic volatility, and stochastic duration models among others. The state variables in this class follow a nonnegative stochastic process that is popular in econometrics for modeling volatility and intensities. In addition to calculating the likelihood, I also show how to perform filtering and smoothing to estimate the latent variables in the model. The procedures in this article can be used for either Bayesian or frequentist estimation of the model’s unknown parameters as well as the latent state variables. Supplementary materials for this article are available online.

Suggested Citation

  • Drew D. Creal, 2017. "A Class of Non-Gaussian State Space Models With Exact Likelihood Inference," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 35(4), pages 585-597, October.
    • Handle: RePEc:taf:jnlbes:v:35:y:2017:i:4:p:585-597
    DOI: 10.1080/07350015.2015.1092977
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    Cited by:

    1. Hong Li & Yang Lu, 2018. "A Bayesian non-parametric model for small population mortality," Post-Print hal-02419000, HAL.
    2. Yang Lu, 2020. "A simple parameter‐driven binary time series model," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 39(2), pages 187-199, March.
    3. Roberto León-González, 2019. "Efficient Bayesian inference in generalized inverse gamma processes for stochastic volatility," Econometric Reviews, Taylor & Francis Journals, vol. 38(8), pages 899-920, September.
    4. Fulop, Andras & Heng, Jeremy & Li, Junye & Liu, Hening, 2022. "Bayesian estimation of long-run risk models using sequential Monte Carlo," Journal of Econometrics, Elsevier, vol. 228(1), pages 62-84.
    5. Tevfik Aktekin & Nicholas G. Polson & Refik Soyer, 2020. "A family of multivariate non‐gaussian time series models," Journal of Time Series Analysis, Wiley Blackwell, vol. 41(5), pages 691-721, September.
    6. Roberto Leon-Gonzalez & Blessings Majoni, 2023. "Exact Likelihood for Inverse Gamma Stochastic Volatility Models," Working Paper series 23-11, Rimini Centre for Economic Analysis.
    7. Andras Fulop & Jeremy Heng & Junye Li, 2022. "Efficient Likelihood-based Estimation via Annealing for Dynamic Structural Macrofinance Models," Papers 2201.01094, arXiv.org.

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