An adaptive resampling scheme for cycle estimation

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.