Smoothness Priors Analysis of Time Series addresses some of the
problems of modeling stationary and nonstationary time series primarily
from a Bayesian stochastic regression "smoothness priors" 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 "particle-path tracing" method in which the distributions
are approximated by many realizations. The methods are applicable for
modeling time series with complex structures.