An adaptive resampling scheme for cycle estimation - Alexandra Mello Schmidt; Dani Gamerman; Ajax Reynaldo Bello Moreira (Institute for Applied Economic Research (ipea), 2015)
Bayesian dynamic linear models (DLM) are useful in time series modelling because of the flexibility that they present in obtaining a good forecast. They are based on a decomposition of the relevant factors which explain the behavior of the series through a series of state parameters. Nevertheless the DLM as developed in West & Harrison (1997) depend on additional quantities, such as the variance of the system disturbances, which, in practice, are unknown. These are refered as hyperparameters of the model. In this paper, DLM with auto-regressive components are used to describe time series showing cyclic behavior. The marginal posterior distribution for state parameters can be obtained by weighing the conditional distribution of state parameters by the marginal distribution of hyperparameters. In most cases the joint distribution of the hyperparameters can be obtained analytically but the marginal distributions of the components can not, thus requiring numerical integration. We propose to obtain samples of the hyperparameters by a variant of the Sampling Importance Resampling (SIR) method. A few applications are made with simulated and real datasets.
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