Computer-Aided Introduction to Econometrics

The advent of low cost computation has made many previously intractable econometric models empirically feasible and computational methods are now realized as an integral part of the theory.
This book provides graduate students and researchers not only with a sound theoretical introduction to the topic, but allows the reader through an internet based interactive computing method to learn from theory to practice the different techniques discussed in the book. Among the theoretical issues presented are linear regression analysis, univariate time series modelling with some interesting extensions such as ARCH models and dimensionality reduction techniques.
The electronic version of the book including all computational possibilites can be viewed at
http://www.xplore-stat.de/ebooks/ebooks.html

Contenu

1 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 Models for Time Series.- 4.6.1 Cointegration.- 4.6.2 Error Correction Models.- 5 Multiplicative SARIMA models.- 5.1 Introduction.- 5.2 Modeling Seasonal Time Series.- 5.2.1 Seasonal ARIMA Models.- 5.2.2 Multiplicative SARIMA Models.- 5.2.3 The Expanded Model.- 5.3 Identification of Multiplicative SARIMA Models.- 5.4 Estimation of Multiplicative SARIMA Models.- 5.4.1 Maximum Likelihood Estimation.- 5.4.2 Setting the Multiplicative SARIMA Model.- 5.4.3 Setting the Expanded Model.- 5.4.4 The Conditional Sum of Squares.- 5.4.5 The Extended ACF.- 5.4.6 The Exact Likelihood.- 6 Auto Regressive Conditional Heteroscedastic Models.- 6.1 Introduction.- 6.2 ARCH(1) Model.- 6.2.1 Conditional and Unconditional Moments of the ARCH(1).- 6.2.2 Estimation for ARCH(1) Process.- 6.3 ARCH(q) Model.- 6.4 Testing Heteroscedasticity and ARCH(1) Disturbances.- 6.4.1 The Breusch-Pagan Test.- 6.4.2 ARCH(1) Disturbance Test.- 6.5 ARCH(1) Regression Model.- 6.6 GARCH(p,q) Model.- 6.6.1 GARCH(1,1) Model.- 6.7 Extensions of ARCH Models.- 6.8 Two Examples of Spanish Financial Markets.- 6.8.1 Ibex35 Data.- 6.8.2 Exchange Rate US Dollar/Spanish Peseta Data (Continued).- 7 Numerical Optimization Methods in Econometrics.- 7.1 Introduction.- 7.2 Solving a Nonlinear Equation.- 7.2.1 Termination of Iterative Methods.- 7.2.2 Newton-Raphson Method.- 7.3 Solving a System of Nonlinear Equations.- 7.3.1 Newton-Raphson Method for Systems.- 7.3.2 Example.- 7.3.3 Modified Newton-Raphson Method for Systems.- 7.3.4 Example.- 7.4 Minimization of a Function: One-dimensional Case.- 7.4.1 Minimum Bracketing.- 7.4.2 Example.- 7.4.3 Parabolic Interpolation.- 7.4.4 Example.- 7.4.5 Golden Section Search.- 7.4.6 Example.- 7.4.7 Brent's Method.- 7.4.8 Example.- 7.4.9 Brent's Method Using First Derivative of a Function..- 7.4.10 Example.- 7.5 Minimization of a Function: Multidimensional Case.- 7.5.1 Neider and Mead's Downhill Simplex Method (Amoeba).- 7.5.2 Example.- 7.5.3 Conjugate Gradient Methods.- 7.5.4 Examples.- 7.5.5 Quasi-Newton Methods.- 7.5.6 Examples.- 7.5.7 Line Minimization.- 7.5.8 Examples.- 7.6 Auxiliary Routines for Numerical Optimization.- 7.6.1 Gradient.- 7.6.2 Examples.- 7.6.3 Jacobian.- 7.6.4 Examples.- 7.6.5 Hessian.- 7.6.6 Example.- 7.6.7 Restriction of a Function to a Line.- 7.6.8 Example.- 7.6.9 Derivative of a Restricted function.- 7.6.10 Example.