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AuthorKitagawa, Genshiro. author
TitleSmoothness Priors Analysis of Time Series [electronic resource] / by Genshiro Kitagawa, Will Gersch
ImprintNew York, NY : Springer New York : Imprint: Springer, 1996
Connect tohttp://dx.doi.org/10.1007/978-1-4612-0761-0
Descript X, 280 p. online resource

SUMMARY

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

1 Introduction -- 1.1 Background -- 1.2 What is in the Book -- 1.3 Time Series Examples -- 2 Modeling Concepts and Methods -- 2.1 Akaikeโ{128}{153}s AIC: Evaluating Parametric Models -- 2.2 Least Squares Regression by Householder Transformation -- 2.3 Maximum Likelihood Estimation and an Optimization Algorithm -- 2.4 State Space Methods -- 3 The Smoothness Priors Concept -- 3.1 Introduction -- 3.2 Background, History and Related Work -- 3.3 Smoothness Priors Bayesian Modeling -- 4 Scalar Least Squares Modeling -- 4.1 Estimating a Trend -- 4.2 The Long AR Model -- 4.3 Transfer Function Estimation -- 5 Linear Gaussian State Space Modeling -- 5.1 Introduction -- 5.2 Standard State Space Modeling -- 5.3 Some State Space Models -- 5.4 Modeling With Missing Observations -- 5.5 Unequally Spaced Observations -- 5.6 An Information Square-Root Filter/Smoother -- 6 Contents General State Space Modeling -- 6.1 Introduction -- 6.2 The General State Space Model -- 6.3 Numerical Synthesis of the Algorithms -- 6.4 The Gaussian Sum-Two Filter Formula Approximation -- 6.5 A Monte Carlo Filtering and Smoothing Method -- 6.6 A Derivation of the Kalman filter -- 7 Applications of Linear Gaussian State Space Modeling -- 7.1 AR Time Series Modeling -- 7.2 Kullback-Leibler Computations -- 7.3 Smoothing Unequally Spaced Data -- 7.4 A Signal Extraction Problem -- 8 Modeling Trends -- 8.1 State Space Trend Models -- 8.2 State Space Estimation of Smooth Trend -- 8.3 Multiple Time Series Modeling: The Common Trend Plus Individual Component AR Model -- 8.4 Modeling Trends with Discontinuities -- 9 Seasonal Adjustment -- 9.1 Introduction -- 9.2 A State Space Seasonal Adjustment Model -- 9.3 Smooth Seasonal Adjustment Examples -- 9.4 Non-Gaussian Seasonal Adjustment -- 9.5 Modeling Outliers -- 9.6 Legends -- 10 Estimation of Time Varying Variance -- 10.1 Introduction and Background -- 10.2 Modeling Time-Varying Variance -- 10.3 The Seismic Data -- 10.4 Smoothing the Periodogram -- 10.5 The Maximum Daily Temperature Data -- 11 Modeling Scalar Nonstationary Covariance Time Series -- 11.1 Introduction -- 11.2 A Time Varying AR Coefficient Model -- 11.3 A State Space Model -- 11.4 PARCOR Time Varying AR Modeling -- 11.5 Examples -- 12 Modeling Multivariate Nonstationary Covariance Time Series -- 12.1 Introduction -- 12.2 The Instantaneous Response-Orthogonal Innovations Model -- 12.3 State Space Modeling -- 12.4 Time Varying PARCOR VAR Modeling -- 12.5 Examples -- 13 Modeling Inhomogeneous Discrete Processes -- 13.1 Nonstationary Discrete Process -- 13.2 Nonstationary Binary Processes -- 13.3 Nonstationary Poisson Process -- 14 Quasi-Periodic Process Modeling -- 14.1 The Quasi-periodic Model -- 14.2 The Wolfer Sunspot Data -- 14.3 The Canadian Lynx Data -- 14.4 Other Examples -- 14.5 Predictive Properties of Quasi-periodic Process Modeling -- 15 Nonlinear Smoothing -- 15.1 Introduction -- 15.2 State Estimation -- 15.3 A One Dimensional Problem -- 15.4 A Two Dimensional Problem -- 16 Other Applications -- 16.1 A Large Scale Decomposition Problem -- 16.2 Markov State Classification -- 16.3 SPVAR Modeling for Spectrum Estimation -- References -- Author Index


Statistics Mathematical analysis Analysis (Mathematics) Statistics Statistics general Analysis



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