Testing for Random Walk Coefficients in Regression and State Space Models

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.