Smoothness Priors in Time Series.

摘要

A variety of time series signal extraction/smoothing problems are considered from a Bayesian smoothness priors point of view. The origin of the subject is a smoothing problem posed by Whittaker (1923). Using a stochastic regression-linear model-Gaussian disturbances framework, we model stationary time series and nonstationary mean and nonstationary covariance time series. Smoothness priors distributions on the model parameters are expressed either in terms of time domain stochastic difference equation or frequency domain constants. A small number of (hyper) parameters specify very complex time series behavior. The critical computation is the likelihood of the Bayesian model. Finally we show a smoothness priors state space - not necessarily Gaussian - not necessarily linear model of nonstationary time series.