Beschreibung
Inhaltsangabe1 Univariate Linear Regression Model.- 1.1 Probability and Data Generating Process.- 1.1.1 Random Variable and Probability Distribution.- 1.1.2 Example.- 1.1.3 Data Generating Process.- 1.1.4 Example.- 1.2 Estimators and Properties.- 1.2.1 Regression Parameters and their Estimation.- 1.2.2 Least Squares Method.- 1.2.3 Example.- 1.2.4 Goodness of Fit Measures.- 1.2.5 Example.- 1.2.6 Properties of the OLS Estimates of a, ß and ?2.- 1.2.7 Examples.- 1.3 Inference.- 1.3.1 Hypothesis Testing about ß.- 1.3.2 Example.- 1.3.3 Testing Hypothesis Based on the Regression Fit.- 1.3.4 Example.- 1.3.5 Hypothesis Testing about ?.- 1.3.6 Example.- 1.3.7 Hypotheses Testing about ?2.- 1.4 Forecasting.- 1.4.1 Confidence Interval for the Point Forecast.- 1.4.2 Example.- 1.4.3 Confidence Interval for the Mean Predictor.- 2 Multivariate Linear Regression Model.- 2.1 Introduction.- 2.2 Classical Assumptions of the MLRM.- 2.2.1 The Systematic Component Assumptions.- 2.2.2 The Random Component Assumptions.- 2.3 Estimation Procedures.- 2.3.1 The Least Squares Estimation.- 2.3.2 The Maximum Likelihood Estimation.- 2.3.3 Example.- 2.4 Properties of the Estimators.- 2.4.1 Finite Sample Properties of the OLS and ML Estimates ofß.- 2.4.2 Finite Sample Properties of the OLS and ML Estimates of ?2.- 2.4.3 Asymptotic Properties of the OLS and ML Estimators of ß.- 2.4.4 Asymptotic Properties of the OLS and ML Estimators of ?2.- 2.4.5 Example.- 2.5 Interval Estimation.- 2.5.1 Interval Estimation of the Coefficients of the MLRM.- 2.5.2 Interval Estimation of ?2.- 2.5.3 Example.- 2.6 Goodness of Fit Measures.- 2.7 Linear Hypothesis Testing.- 2.7.1 Hypothesis Testing about the Coefficients.- 2.7.2 Hypothesis Testing about a Coefficient of the MLRM.- 2.7.3 Testing the Overall Significance of the Model.- 2.7.4 Testing Hypothesis about ?2.- 2.7.5 Example.- 2.8 Restricted and Unrestricted Regression.- 2.8.1 Restricted Least Squares and Restricted Maximum Likelihood Estimators.- 2.8.2 Finite Sample Properties of the Restricted Estimator Vector.- 2.8.3 Example.- 2.9 Three General Test Procedures.- 2.9.1 Likelihood Ratio Test (LR).- 2.9.2 The Wald Test (W).- 2.9.3 Lagrange Multiplier Test (LM).- 2.9.4 Relationships and Properties of the Three General Testing Procedures.- 2.9.5 The Three General Testing Procedures in the MLRM Context.- 2.9.6 Example.- 2.10 Dummy Variables.- 2.10.1 Models with Changes in the Intercept.- 2.10.2 Models with Changes in some Slope Parameters.- 2.10.3 Models with Changes in all the Coefficients.- 2.10.4 Example.- 2.11 Forecasting.- 2.11.1 Point Prediction.- 2.11.2 Interval Prediction.- 2.11.3 Measures of the Accuracy of Forecast.- 2.11.4 Example.- 3 Dimension Reduction and Its Applications.- 3.1 Introduction.- 3.1.1 Real Data Sets.- 3.1.2 Theoretical Consideration.- 3.2 Average Outer Product of Gradients and its Estimation.- 3.2.1 The Simple Case.- 3.2.2 The Varying-coefficient Model.- 3.3 A Unified Estimation Method.- 3.3.1 The Simple Case.- 3.3.2 The Varying-coefficient Model.- 3.4 Number of E.D.R. Directions.- 3.5 The Algorithm.- 3.6 Simulation Results.- 3.7 Applications.- 3.8 Conclusions and Further Discussion.- 3.9 Appendix. Assumptions and Remarks.- 4 Univariate Time Series Modelling.- 4.1 Introduction.- 4.2 Linear Stationary Models for Time Series.- 4.2.1 White Noise Process.- 4.2.2 Moving Average Model.- 4.2.3 Autoregressive Model.- 4.2.4 Autoregressive Moving Average Model.- 4.3 Nonstationary Models for Time Series.- 4.3.1 Nonstationary in the Variance.- 4.3.2 Nonstationarity in the Mean.- 4.3.3 Testing for Unit Roots and Stationarity.- 4.4 Forecasting with ARIMA Models.- 4.4.1 The Optimal Forecast.- 4.4.2 Computation of Forecasts.- 4.4.3 Eventual Forecast Functions.- 4.5 ARIMA Model Building.- 4.5.1 Inference for the Moments of Stationary Processes.- 4.5.2 Identification of ARIMA Models.- 4.5.3 Parameter Estimation.- 4.5.4 Diagnostic Checking.- 4.5.5 Model Selection Criteria.- 4.5.6 Example: European Union G.D.P.- 4.6 Regression Mode
