Readings in Unobserved Components Models

This book presents a collection of readings which give the reader an idea of the nature and scope of unobserved components (UC) models and the methods used to deal with them. It contains four parts, three of which concern recent theoretical developments in classical and Bayesian estimation of linear, nonlinear, and non Gaussian UC models, signal extraction and testing, and one is devoted to selected econometric applications. The first part focuses on the linear state space model; the readings provide insight on prediction theory, signal extraction, and likelihood inference for non stationary and non invertible processes, diagnostic checking, and the use of state space methods for spline smoothing. Part II deals with applications of linear UC models to various estimation problems concerning economic time series, such as trend-cycle decompositions, seasonal adjustment, and the modelling of the serial correlation induced by survey sample design. The issues involved in testing in linear UC models are the theme of part III, which considers tests concerned with whether or not certain variance parameters are zero, with special reference to stationarity tests. Finally, part IV is devoted to the advances concerning classical and Bayesian inference for non linear and non Gaussian state space models, an area that has been evolving very rapidly during the last decade, paralleling the advances in computational inference using stochastic simulation techniques. The book is intended to give a relatively self-contained presentation of the methods and applicative issues. For this purpose, each part comes with an introductory chapter by the editors that provides a unified view of the literature and the many important developments that have occurred in the last years.

Table of Contents:
SIGNAL EXTRACTION AND LIKELIHOOD INFERENCE FOR LINEAR UC MODELS ; 1. Introduction ; 2. Prediction Theory for Autoregressive-Moving Average Processes ; 3. Exact Initial Kalman Filtering and Smoothing for Non-stationary Time Series Models ; 4. Smoothing and Interpolation with the State Space Model ; 5. Diagnostic Checking of Unobserved Components in Time Series Models ; 6. Nonparametric Spline Regression with Autoregressive Moving Average Errors ; UNOBSERVED COMPONENTS IN ECONOMIC TIME SERIES ; 7. Introduction ; 8. Univariate Detrending Methods with Stochastic Trends ; 9. Detrending, Stylized Facts and the Business Cycle ; 10. Stochastic Linear Trends, Models and Estimators ; 11. Estimation and Seasonal Adjustment of Population Means Using Data from Repeated Surveys ; 12. The Modelling and Seasonal Adjustment of Weekly Observations ; TESTING IN UNOBSERVED COMPONENTS MODELS ; 13. Introduction ; 14. Testing for Deterministic Linear Trends in a Times Series ; 15. Are Seasonal Patterns Stable Over Time? A Test for Seasonal Stability ; NON-LINEAR AND NON- GAUSSIAN MODELS ; 16. Introduction ; 17. Times Series Models for Count Data or Qualitative Observations ; 18. On Gibbs Sampling for State Space Models ; 19. The Simulation Smoother ; 20. Likelihood Analysis of Non-Gaussian Measurement Time Series ; 21. Time Series Analysis of Non-Gaussian Observations based on State Space Models from both Classical and Bayesian Perspectives ; 22. Stochastic Volatility: Liklihood Inference and Comparison with ARCH Models ; 23. On Sequential Monte Carlo Sampling Methods for Bayesian Filtering