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An adaptive resampling scheme for cycle estimation

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  • Alexandra Mello Schmidt
  • Dani Gamerman
  • Ajax Moreira

Abstract

Bayesian dynamic linear models (DLMs) are useful in time series modelling, because of the flexibility that they off er for obtaining a good forecast. They are based on a decomposition of the relevant factors which explain the behaviour of the series through a series of state parameters. Nevertheless, the DLM as developed by West and Harrison depend on additional quantities, such as the variance of the system disturbances, which, in practice, are unknown. These are referred to here as 'hyper-parameters' of the model. In this paper, DLMs with autoregressive components are used to describe time series that show cyclic behaviour. The marginal posterior distribution for state parameters can be obtained by weighting the conditional distribution of state parameters by the marginal distribution of hyper-parameters. In most cases, the joint distribution of the hyperparameters can be obtained analytically but the marginal distributions of the components cannot, so requiring numerical integration. We propose to obtain samples of the hyperparameters by a variant of the sampling importance resampling method. A few applications are shown with simulated and real data sets.

Suggested Citation

  • Alexandra Mello Schmidt & Dani Gamerman & Ajax Moreira, 1999. "An adaptive resampling scheme for cycle estimation," Journal of Applied Statistics, Taylor & Francis Journals, vol. 26(5), pages 619-641.
    • Handle: RePEc:taf:japsta:v:26:y:1999:i:5:p:619-641
    DOI: 10.1080/02664769922287
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    References listed on IDEAS

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    1. Danaher, Peter J. & Dagger, Tracey S. & Smith, Michael S., 2011. "Forecasting television ratings," International Journal of Forecasting, Elsevier, vol. 27(4), pages 1215-1240, October.
    2. Lopes, Hedibert Freitas & Moreira, Ajax R. Bello & Schmidt, Alexandra Mello, 1999. "Hyperparameter estimation in forecast models," Computational Statistics & Data Analysis, Elsevier, vol. 29(4), pages 387-410, February.
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    Cited by:

    1. Huerta, Gabriel & Lopes, Hedibert Freitas, 2000. "Bayesian forecasting and inference in latent structure for the Brazilian Industrial Production Index," Brazilian Review of Econometrics, Sociedade Brasileira de Econometria - SBE, vol. 20(1), May.
    2. Gamerman, Dani & Moreira, Ajax R. B. & Rue, Havard, 2003. "Space-varying regression models: specifications and simulation," Computational Statistics & Data Analysis, Elsevier, vol. 42(3), pages 513-533, March.
    3. Ajax R. B. Moreira & Dani Gamerman, 2015. "Bayesian Analysis of Econometric Time Series Models Using Hybrid Integration Rules," Discussion Papers 0105, Instituto de Pesquisa Econômica Aplicada - IPEA.
    4. Lopes, Hedibert Freitas & Moreira, Ajax R. Bello & Schmidt, Alexandra Mello, 1999. "Hyperparameter estimation in forecast models," Computational Statistics & Data Analysis, Elsevier, vol. 29(4), pages 387-410, February.

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