Smoothness Priors Analysis of Time Series addresses some of the problems of modeling stationary and nonstationary time series primarily from a Bayesian stochastic regression qsmoothness priorsq state space point of view. Prior distributions on model coefficients are parametrized by hyperparameters. Maximizing the likelihood of a small number of hyperparameters permits the robust modeling of a time series with relatively complex structure and a very large number of implicitly inferred parameters. The critical statistical ideas in smoothness priors are the likelihood of the Bayesian model and the use of likelihood as a measure of the goodness of fit of the model. The emphasis is on a general state space approach in which the recursive conditional distributions for prediction, filtering, and smoothing are realized using a variety of nonstandard methods including numerical integration, a Gaussian mixture distribution-two filter smoothing formula, and a Monte Carlo qparticle-path tracingq method in which the distributions are approximated by many realizations. The methods are applicable for modeling time series with complex structures.Recursive formulas for prediction, filtering and smoothing for the nonlinear state space model are shown. The performance of the method is illustrated by the analyses of both a one dimensional and a two dimensional example that ... The conventional Gaussian sum filter has several technical difficulties in its implementation.
|Title||:||Smoothness Priors Analysis of Time Series|
|Author||:||Genshiro Kitagawa, Will Gersch|
|Publisher||:||Springer Science & Business Media - 2012-12-06|