Smoothness Priors Analysis Of Time Series (lecture Notes In Statistics)
by Genshiro Kitagawa /
2013 / English / PDF
8.9 MB Download
Smoothness Priors Analysis of Time Series
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.
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.
