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…mehr
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 coefficientsvaries over time.
1 Introduction.- 2 The Linear State Space Model.- 2.1 The Model Set-up.- 2.2 Some Basic Results.- 2.3 Interpretation of the State Space Model.- 2.4 The Kalman Filter and Smoother.- 2.5 Estimation of the Hyperparameters.- 2.6 An Illustrative Example.- 2.7 Forecasting.- 3 Exact Tests for Univariate Random Walk Coefficients.- 3.1 The Testing Problem.- 3.2 An Exact F-Test.- 3.3 A Point Optimal Invariant Test.- 3.4 The Locally Best Invariant Test.- 3.5 Simulation Study.- 3.6 Appendix: Determination of Critical Values.- 4 Asymptotic Tests for Univariate Random Walk Coefficients in Models with Stationary Regressors.- 4.1 Introduction.- 4.2 Asymptotic Distribution of the LM/LBI Test.- 4.3 The Hansen Test.- 4.4 The Modified Hansen Test.- 4.5 The Test of Leybourne k McCabe.- 4.6 Simulation Study.- 5 Asymptotic Tests for Univariate Random Walk Coefficients in Models with Non-Stationary Regressors.- 5.1 Introduction.- 5.2 The Model and the Estimators.- 5.3 Asymptotic Distribution of the LM/LBI Test in the Presence of I(1) Regressors.- 5.4 Asymptotic Distribution of Test Statistics Based on OLS Estimators.- 5.5 Asymptotic Distribution of Test Statistics Based on Asymptotically Efficient Estimators.- 5.6 Testing the Constancy of the Intercept.- 5.7 Simulation Study.- 5.8 Tests with Polynomial Regressors.- 6 Testing Trend Stationarity Against Difference Stationarity in Time Series.- 6.1 Introduction.- 6.2 The KPSS Test.- 6.3 The Test of Leybourne & McCabe.- 6.4 The Choi Test.- 6.5 The Tsay Test.- 6.6 POI and LBI Tests.- 6.7 Simulation Study.- 7 Testing for Multivariate Random Walk Coefficients in Regression Models.- 7.1 The Testing Problem.- 7.2 Exact Tests.- 7.3 Simulation Study: Exact Tests.- 7.4 Asymptotic Tests in Models with Stationary Regressors.- 7.5 Simulation Study: Stationary Regressors.- 7.6 Asymptotic Tests in Models with Integrated Regressors.- 7.7 Simulation Study: Integrated Regressors.- 8 Testing for Random Walk Coefficients in the Presence of Varying Coefficients Under H0.- 8.1 The Testing Problem.- 8.2 Asymptotic Tests.- 8.3 Simulation Study.- 9 The Term Structure of German Interest Rates - Testing the Expectations Hypothesis.- 9.1 The Data.- 9.2 Tests.- 9.3 Estimation of State Space Models.- 9.4 Conclusions.- 10 Résumé and Prospects.- References.
1 Introduction.- 2 The Linear State Space Model.- 2.1 The Model Set-up.- 2.2 Some Basic Results.- 2.3 Interpretation of the State Space Model.- 2.4 The Kalman Filter and Smoother.- 2.5 Estimation of the Hyperparameters.- 2.6 An Illustrative Example.- 2.7 Forecasting.- 3 Exact Tests for Univariate Random Walk Coefficients.- 3.1 The Testing Problem.- 3.2 An Exact F-Test.- 3.3 A Point Optimal Invariant Test.- 3.4 The Locally Best Invariant Test.- 3.5 Simulation Study.- 3.6 Appendix: Determination of Critical Values.- 4 Asymptotic Tests for Univariate Random Walk Coefficients in Models with Stationary Regressors.- 4.1 Introduction.- 4.2 Asymptotic Distribution of the LM/LBI Test.- 4.3 The Hansen Test.- 4.4 The Modified Hansen Test.- 4.5 The Test of Leybourne k McCabe.- 4.6 Simulation Study.- 5 Asymptotic Tests for Univariate Random Walk Coefficients in Models with Non-Stationary Regressors.- 5.1 Introduction.- 5.2 The Model and the Estimators.- 5.3 Asymptotic Distribution of the LM/LBI Test in the Presence of I(1) Regressors.- 5.4 Asymptotic Distribution of Test Statistics Based on OLS Estimators.- 5.5 Asymptotic Distribution of Test Statistics Based on Asymptotically Efficient Estimators.- 5.6 Testing the Constancy of the Intercept.- 5.7 Simulation Study.- 5.8 Tests with Polynomial Regressors.- 6 Testing Trend Stationarity Against Difference Stationarity in Time Series.- 6.1 Introduction.- 6.2 The KPSS Test.- 6.3 The Test of Leybourne & McCabe.- 6.4 The Choi Test.- 6.5 The Tsay Test.- 6.6 POI and LBI Tests.- 6.7 Simulation Study.- 7 Testing for Multivariate Random Walk Coefficients in Regression Models.- 7.1 The Testing Problem.- 7.2 Exact Tests.- 7.3 Simulation Study: Exact Tests.- 7.4 Asymptotic Tests in Models with Stationary Regressors.- 7.5 Simulation Study: Stationary Regressors.- 7.6 Asymptotic Tests in Models with Integrated Regressors.- 7.7 Simulation Study: Integrated Regressors.- 8 Testing for Random Walk Coefficients in the Presence of Varying Coefficients Under H0.- 8.1 The Testing Problem.- 8.2 Asymptotic Tests.- 8.3 Simulation Study.- 9 The Term Structure of German Interest Rates - Testing the Expectations Hypothesis.- 9.1 The Data.- 9.2 Tests.- 9.3 Estimation of State Space Models.- 9.4 Conclusions.- 10 Résumé and Prospects.- References.
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