Some applications of smoothness priors in time series

A variety of time series 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). Stationary time series and nonstationary mean and nonstationary covariance times series are modeled from a stochastic regression-linear model-Gaussian disturbances framework. Smoothness priors distributions on the model parameters are expressed either in terms of time domain stochastic difference equation or frequency domain constraints. A small number of (hyper) parameters specify very complex time series behavior. The critical computation is the likelihood of the Bayesian model. The computations are realized either by Householder transformation algorithms or Kalman filter state space model methods.