Ebook: 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.

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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.

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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.
Content:
Front Matter....Pages i-x
Introduction....Pages 1-8
Modeling Concepts and Methods....Pages 9-26
The Smoothness Priors Concept....Pages 27-32
Scalar Least Squares Modeling....Pages 33-53
Linear Gaussian State Space Modeling....Pages 55-65
General State Space Modeling....Pages 67-89
Applications of Linear Gaussian State Space Modeling....Pages 91-104
Modeling Trends....Pages 105-121
Seasonal Adjustment....Pages 123-135
Estimation of Time Varying Variance....Pages 137-145
Modeling Scalar Nonstationary Covariance Time Series....Pages 147-160
Modeling Multivariate Nonstationary Covariance Time Series....Pages 161-179
Modeling Inhomogeneous Discrete Processes....Pages 181-187
Quasi-Periodic Process Modeling....Pages 189-200
Nonlinear Smoothing....Pages 201-212
Other Applications....Pages 213-230
Back Matter....Pages 231-263

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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.
Content:
Front Matter....Pages i-x
Introduction....Pages 1-8
Modeling Concepts and Methods....Pages 9-26
The Smoothness Priors Concept....Pages 27-32
Scalar Least Squares Modeling....Pages 33-53
Linear Gaussian State Space Modeling....Pages 55-65
General State Space Modeling....Pages 67-89
Applications of Linear Gaussian State Space Modeling....Pages 91-104
Modeling Trends....Pages 105-121
Seasonal Adjustment....Pages 123-135
Estimation of Time Varying Variance....Pages 137-145
Modeling Scalar Nonstationary Covariance Time Series....Pages 147-160
Modeling Multivariate Nonstationary Covariance Time Series....Pages 161-179
Modeling Inhomogeneous Discrete Processes....Pages 181-187
Quasi-Periodic Process Modeling....Pages 189-200
Nonlinear Smoothing....Pages 201-212
Other Applications....Pages 213-230
Back Matter....Pages 231-263
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