Multiple Time Series Modeling Using the SAS® VARMAX Procedure
by Anders Milhoj
Multiple Time Series Modeling Using the SAS VARMAX Procedure
- 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
Multiple Time Series Modeling
Using the SAS® VARMAX Procedure
Anders Milhøj
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