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Regression and state space models with time varying coefficients are treated in a thorough manner. State space models are introduced as a means to model time varying regression coefficients. The Kalman filter and smoother recursions are explained in an easy to understand fashion. The main part of the book deals with testing the null hypothesis of constant regression coefficients against the alternative that they follow a random walk. Different exact and large sample tests are presented and extensively compared based on Monte Carlo studies, so that the reader is guided in the question which test to choose in a particular situation. Moreover, different new tests are proposed which are suitable in situations with autocorrelated or heteroskedastic errors. Additionally, methods are developed to test for the constancy of regression coefficients in situations where one knows already that some coefficients follow a random walk, thereby one is enabled to find out which of the coefficients varies over time.
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Front Matter
Introduction
The Linear State Space Model
Exact Tests for Univariate Random Walk Coefficients
Asymptotic Tests for Univariate Random Walk Coefficients in Models with Stationary Regressors
Asymptotic Tests for Univariate Random Walk Coefficients in Models with Non-Stationary Regressors
Testing Trend Stationarity Against Difference Stationarity in Time Series
Testing for Multivariate Random Walk Coefficients in Regression Models
Testing for Random Walk Coefficients in the Presence of Varying Coefficients Under H 0
The Term Structure of German Interest Rates — Testing the Expectations Hypothesis
Résumé and Prospects
Back Matter