- About This Book
- About The Authors
- Acknowledgment
- Chapter 1: Introduction
- Chapter 2: Regression Analysis for Time Series Data
- Chapter 3: Regression Analysis with Autocorrelated Errors
- Chapter 4: Regression Models for Differenced Series
- Introduction
- Regression Model for the Differenced Series
- Reverted Regression
- Inclusion of the Lagged Independent Variable in the Model
- Two Lags of the Independent Variables
- Inclusion of the Lagged Dependent Variable in the Regression
- How to Interpret a Model with a Lagged Dependent Variable
- Conclusions about the Models in Chapters 2, 3, and 4
- Chapter 5: Tests for Differencing Time Series
- Chapter 6: Models for Univariate Time Series
- Chapter 7: Use of the VARMAX Procedure to Model Univariate Series
- Introduction
- Wage-Price Time Series
- PROC VARMAX Applied to the Wage Series
- PROC VARMAX Applied to the Differenced Wage Series
- Estimation of the AR(2) Model
- Check of the Fit of the AR(2) Model
- PROC VARMAX Applied to the Price Series
- PROC VARMAX Applied to the Number of Cows Series
- PROC VARMAX Applied to the Series of Milk Production
- A Simple Moving Average Model of Order 1
- Conclusion
- Chapter 8: Models for Multivariate Time Series
- Chapter 9: Use of the VARMAX Procedure to Model Multivariate Series
- Introduction
- Use of PROC VARMAX to Model Multivariate Time Series
- Fit of a Fourth-Order Autoregressive Model
- Residual Autocorrelation in a VARMA(2,0) Model
- Distribution of the Residuals in a VARMA(2,0) Model
- Identification of Outliers
- Use of a VARMA Model for Milk Production and the Number of Cows
- Conclusion
- Chapter 10: Exploration of the Output
- Chapter 11: Causality Tests for the Danish Egg Market
- Introduction
- The Danish Egg Market
- Formulation of the VARMA Model for the Egg Market Data
- Causality Tests of the Total Market Series
- Granger Causality Tests in the VARMAX Procedure
- Causality Tests of the Production Series
- Causality Tests That Use Extended Information Sets
- Estimation of a Final Causality Model
- Fit of the Final Model
- Conclusion
- Chapter 12: Bayesian Vector Autoregressive Models
- Chapter 13: Vector Error Correction Models
- Introduction
- The Error Correction Model
- A Simple Example: The Price of Potatoes in Ohio and Pennsylvania
- Estimated Error Correction Parameters
- Theory for Testing Hypotheses on β Parameters
- Tests of Hypotheses on the β Parameters Using PROC VARMAX
- Tests of Hypotheses on the α Parameters by PROC VARMAX
- The TEST Statement for Hypotheses on the α Parameters
- The RESTRICT Statement for the β Parameters
- Restrictions on Both α Parameters and β Parameters
- Properties of the Final Model
- Conclusion
- Chapter 14: Cointegration
- Introduction
- Test for a Cointegration Relation in the Bivariate Case
- Cointegration Test Using PROC VARMAX for Two Price Series
- Cointegration Tests in a Five-Dimensional Series
- Use of the RESTRICT Statement to Determine the Form of the Model
- Stock-Watson Test for Common Trends for Five Series
- A Rank 4 Model for Five Series Specified with Restrictions
- Conclusion
- Chapter 15: Univariate GARCH Models
- Chapter 16: Multivariate GARCH Models
- Chapter 17: Multivariate VARMA-GARCH Models
- References
- Index
About the Author
Anders Milhøj is associate professor in the Department of Economics at the University of Copenhagen, where he conducts research and lectures on applied statistics topics including survey sampling, regression analysis, time series analysis, and factor analysis. A SAS user since 1984, he employs a variety of SAS procedures in his work, such as SAS/STAT, SAS/IML, SAS/ETS, and SAS/OR. He holds university degrees in statistics and mathematics, as well as a Ph.D. in statistics, all from the University of Copenhagen.
Learn more about this author by visiting his author page at http://support.sas.com/milhoj. There you can download free book excerpts, access example code and data, read the latest reviews, get updates, and more.
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