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Tweedie compound Poisson multivariate state space models for semicontinuous time series

Author

Listed:
  • Xingde Duan

    (Guizhou University of Finance and Economics)

  • Renjun Ma

    (University of New Brunswick)

  • Xiaolei Zhang

    (Yunnan Normal University)

Abstract

Various approaches have been developed to analyze univariate semicontinuous time series data in the literature, whereas analysis of multivariate semicontinuous data has recently become an area of active research. However, there is apparently little, if any, literature on combining these two aspects to model multivariate semicontinuous time series data with covariates. In this paper, we introduce a family of multivariate state space models for semicontinuous time series data by incorporating serially correlated multivariate distribution-free random effects into Tweedie compound Poisson regression model. This model can flexibly accommodate unstructured covariance structures, skewness and zero-inflation. Unlike two-part modelling models, our model maintains natural temporal and multivariate structures of the data and characterizes the effects of covariates on the overall mean of the multivariate semicontinuous time series directly. An optimal estimation of our model has been developed using the orthodox best linear unbiased predictors of the serially correlated multivariate random effects. The usefulness of our approach is illustrated through the analysis of monthly national financing data in China and simulation studies.

Suggested Citation

  • Xingde Duan & Renjun Ma & Xiaolei Zhang, 2025. "Tweedie compound Poisson multivariate state space models for semicontinuous time series," Statistical Papers, Springer, vol. 66(4), pages 1-28, June.
    • Handle: RePEc:spr:stpapr:v:66:y:2025:i:4:d:10.1007_s00362-025-01703-z
    DOI: 10.1007/s00362-025-01703-z
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    References listed on IDEAS

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    1. Renjun Ma, 2003. "Random effects Cox models: A Poisson modelling approach," Biometrika, Biometrika Trust, vol. 90(1), pages 157-169, March.
    2. Renjun Ma & Bent Jørgensen, 2007. "Nested generalized linear mixed models: an orthodox best linear unbiased predictor approach," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(4), pages 625-641, September.
    3. Wagner Hugo Bonat & Bent Jørgensen, 2016. "Multivariate covariance generalized linear models," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 65(5), pages 649-675, November.
    4. Šárka Hudecová & Michal Pešta, 2025. "Hurdle GARCH models for nonnegative time series," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 79(1), February.
    5. Wang, Xiaoqing & Feng, Xiangnan & Song, Xinyuan, 2020. "Joint analysis of semicontinuous data with latent variables," Computational Statistics & Data Analysis, Elsevier, vol. 151(C).
    6. Frees, Edward W. & Jin, Xiaoli & Lin, Xiao, 2013. "Actuarial Applications of Multivariate Two-Part Regression Models," Annals of Actuarial Science, Cambridge University Press, vol. 7(2), pages 258-287, September.
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