Smoothness Priors Analysis of Time SeriesSmoothness 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. |
Contents
| 1 | |
Modeling Concepts and Methods | 9 |
3 | 19 |
The Smoothness Priors Concept | 27 |
Scalar Least Squares Modeling | 33 |
Transfer Function Estimation | 44 |
Linear Gaussian State Space Modeling | 55 |
General State Space Modeling | 67 |
Estimation of Time Varying Variance | 137 |
Modeling Scalar Nonstationary Covariance Time Series | 147 |
Modeling Multivariate Nonstationary Covariance Time Series | 161 |
Modeling Inhomogeneous Discrete Processes | 181 |
QuasiPeriodic Process Modeling | 189 |
Nonlinear Smoothing | 201 |
Other Applications | 213 |
| 231 | |
Applications of Linear Gaussian State Space Modeling | 91 |
Modeling Trends | 105 |
Seasonal Adjustment | 123 |
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Common terms and phrases
AIC best model Akaike algorithm application approach approximation assumed autoregressive model Bayesian Canadian lynx Chapter coefficients common trend computed covariance matrix covariance time series density function density matrix earthquake equation example extended Kalman filter Ey log filtering and smoothing frequency Gaussian model Gersch Householder transformation hyperparameter innovations variance instantaneous interval Kalman filter Kitagawa KL number Kullback-Leibler least squares log-likelihood long AR model maximum likelihood estimate mean time series model order modeling method Monte Carlo multivariate non-Gaussian nonstationary covariance nonstationary mean normally distributed observation noise obtained Original and Trend outliers p(xn p(yn PARCORS periodogram posterior power spectral density prediction problem quasi-periodic recursive regression S-wave scalar Section series analysis series modeling shown in Figure signal simulated data smoother smoothness priors constraints smoothness priors modeling space model spectrum estimation stationary time series Statist stochastic system noise trend model TVVAR vector Уп