Applied Econometric Time Series Third Edition Walter Enders, University of Alabama Copyright © 2010 John Wiley & Sons, Inc.

Chapter 4 MODELS WITH TREND

1. DETERMINISTIC AND STOCHASTIC TRENDS The Random Walk Model The Random Walk Plus Drift Model Generalizations of the Stochastic Trend Model

2. REMOVING THE TREND Differencing Detrending Difference versus Trend-Stationary Models Are There Business Cycles? The Trend in Real GDP

3. UNIT ROOTS AND REGRESSION RESIDUALS

4. THE MONTE CARLO METHOD Monte Carlo Experiments Example of the Monte Carlo Method Generating the Dickey–Fuller Distribution

5. DICKEY–FULLER TESTS An Example

6. EXAMPLES OF THE DICKEY–FULLER TEST Quarterly Real U.S. GDP Unit Roots and Purchasing Power Parity

7. EXTENSIONS OF THE DICKEY–FULLER TEST Selection of the Lag Length The Test with MA Components Lag Lengths and Negative MA Terms Multiple Roots Seasonal Unit Roots

8. STRUCTURAL CHANGE Perron’s Test for Structural Change Perron’s Test and Real Output Tests with Simulated Data

9. POWER AND THE DETERMINISTIC REGRESSORS Determination of the Deterministic Regressors

10. TESTS WITH MORE POWER An Example

11. PANEL UNIT ROOT TESTS Limitations of the Panel Unit Root Test

12. TRENDS AND UNIVARIATE DECOMPOSITIONS The General ARIMA (p, 1, q) Model The Unobserved Components Decomposition The Hodrick–Prescott Decomposition

13. SUMMARY AND CONCLUSIONS

APPENDIX 4.1: THE BOOTSTRAP Bootstrapping Regression Coefficients

APPENDIX 4.2: DETERMINATION OF THE DETERMINISTIC REGRESSORS GDP and Unit Roots