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Chapter 9

Dynamic Models, Autocorrelation and Forecasting. Chapter 9. Prepared by Vera Tabakova, East Carolina University. Chapter 9: Dynamic Models, Autocorrelation and Forecasting. 9.1 Introduction 9.2 Lags in the Error Term: Autocorrelation 9.3 Estimating an AR(1) Error Model

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Chapter 9

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  1. Dynamic Models, Autocorrelation and Forecasting Chapter 9 Prepared by Vera Tabakova, East Carolina University

  2. Chapter 9: Dynamic Models, Autocorrelation and Forecasting • 9.1 Introduction • 9.2 Lags in the Error Term: Autocorrelation • 9.3 Estimating an AR(1) Error Model • 9.4 Testing for Autocorrelation • 9.5 An Introduction to Forecasting: Autoregressive Models • 9.6 Finite Distributed Lags • 9.7 Autoregressive Distributed Lag Models Principles of Econometrics, 3rd Edition

  3. 9.1 Introduction Figure 9.1 Principles of Econometrics, 3rd Edition

  4. 9.1 Introduction Principles of Econometrics, 3rd Edition

  5. 9.1 Introduction Figure 9.2(a) Time Series of a Stationary Variable Principles of Econometrics, 3rd Edition

  6. 9.1 Introduction Figure 9.2(b) Time Series of a Nonstationary Variable that is ‘Slow Turning’ or ‘Wandering’ Principles of Econometrics, 3rd Edition

  7. 9.1 Introduction Figure 9.2(c) Time Series of a Nonstationary Variable that ‘Trends’ Principles of Econometrics, 3rd Edition

  8. 9.2 Lags in the Error Term: Autocorrelation 9.2.1 Area Response Model for Sugar Cane Principles of Econometrics, 3rd Edition

  9. 9.2.2 First-Order Autoregressive Errors Principles of Econometrics, 3rd Edition

  10. 9.2.2 First-Order Autoregressive Errors Principles of Econometrics, 3rd Edition

  11. 9.2.2 First-Order Autoregressive Errors Principles of Econometrics, 3rd Edition

  12. 9.2.2 First-Order Autoregressive Errors Principles of Econometrics, 3rd Edition

  13. 9.2.2 First-Order Autoregressive Errors Figure 9.3 Least Squares Residuals Plotted Against Time Principles of Econometrics, 3rd Edition

  14. 9.2.2 First-Order Autoregressive Errors Principles of Econometrics, 3rd Edition

  15. 9.3 Estimating an AR(1) Error Model The existence of AR(1) errors implies: • The least squares estimator is still a linear and unbiased estimator, but it is no longer best. There is another estimator with a smaller variance. • The standard errors usually computed for the least squares estimator are incorrect. Confidence intervals and hypothesis tests that use these standard errors may be misleading. Principles of Econometrics, 3rd Edition

  16. 9.3 Estimating an AR(1) Error Model Sugar cane example The two sets of standard errors, along with the estimated equation are: The 95% confidence intervals for β2 are: Principles of Econometrics, 3rd Edition

  17. 9.3.2 Nonlinear Least Squares Estimation Principles of Econometrics, 3rd Edition

  18. 9.3.2 Nonlinear Least Squares Estimation Principles of Econometrics, 3rd Edition

  19. 9.3.2a Generalized Least Squares Estimation It can be shown that nonlinear least squares estimation of (9.24) is equivalent to using an iterative generalized least squares estimator called the Cochrane-Orcutt procedure. Details are provided in Appendix 9A. Principles of Econometrics, 3rd Edition

  20. 9.3.3 Estimating a More General Model Principles of Econometrics, 3rd Edition

  21. 9.4 Testing for Autocorrelation 9.4.1 Residual Correlogram Principles of Econometrics, 3rd Edition

  22. 9.4 Testing for Autocorrelation 9.4.1 Residual Correlogram Principles of Econometrics, 3rd Edition

  23. 9.4.1 Residual Correlogram Figure 9.4 Correlogram for Least Squares Residuals from Sugar Cane Example Principles of Econometrics, 3rd Edition

  24. 9.4.1 Residual Correlogram Principles of Econometrics, 3rd Edition

  25. 9.4.1 Residual Correlogram Figure 9.5 Correlogram for Nonlinear Least Squares Residualsfrom Sugar Cane Example Principles of Econometrics, 3rd Edition

  26. 9.4.2 A Lagrange Multiplier Test Principles of Econometrics, 3rd Edition

  27. 9.4.2 A Lagrange Multiplier Test Principles of Econometrics, 3rd Edition

  28. 9.5 An Introduction to Forecasting: Autoregressive Models Principles of Econometrics, 3rd Edition

  29. 9.5 An Introduction to Forecasting: Autoregressive Models Figure 9.6 Correlogram for Least Squares Residuals fromAR(3) Model for Inflation Principles of Econometrics, 3rd Edition

  30. 9.5 An Introduction to Forecasting: Autoregressive Models Principles of Econometrics, 3rd Edition

  31. 9.5 An Introduction to Forecasting: Autoregressive Models Principles of Econometrics, 3rd Edition

  32. 9.5 An Introduction to Forecasting: Autoregressive Models Principles of Econometrics, 3rd Edition

  33. 9.5 An Introduction to Forecasting: Autoregressive Models Principles of Econometrics, 3rd Edition

  34. 9.5 An Introduction to Forecasting: Autoregressive Models Principles of Econometrics, 3rd Edition

  35. 9.6 Finite Distributed Lags Principles of Econometrics, 3rd Edition

  36. 9.6 Finite Distributed Lags Principles of Econometrics, 3rd Edition

  37. 9.6 Finite Distributed Lags Principles of Econometrics, 3rd Edition

  38. 9.7 Autoregressive Distributed Lag Models Principles of Econometrics, 3rd Edition

  39. 9.7 Autoregressive Distributed Lag Models Figure 9.7 Correlogram for Least Squares Residuals fromFinite Distributed Lag Model Principles of Econometrics, 3rd Edition

  40. 9.7 Autoregressive Distributed Lag Models Principles of Econometrics, 3rd Edition

  41. 9.7 Autoregressive Distributed Lag Models Figure 9.8 Correlogram for Least Squares Residuals from Autoregressive Distributed Lag Model Principles of Econometrics, 3rd Edition

  42. 9.7 Autoregressive Distributed Lag Models Principles of Econometrics, 3rd Edition

  43. 9.7 Autoregressive Distributed Lag Models Figure 9.9 Distributed Lag Weights for Autoregressive Distributed Lag Model Principles of Econometrics, 3rd Edition

  44. Keywords • autocorrelation • autoregressive distributed lag models • autoregressive error • autoregressive model • correlogram • delay multiplier • distributed lag weight • dynamic models • finite distributed lag • forecast error • forecasting • HAC standard errors • impact multiplier • infinite distributed lag • interim multiplier • lag length • lagged dependent variable • LM test • nonlinear least squares • sample autocorrelation function • standard error of forecast error • total multiplier • form of LM test Principles of Econometrics, 3rd Edition

  45. Chapter 9 Appendices • Appendix 9A Generalized Least Squares Estimation • Appendix 9B The Durbin Watson Test • Appendix 9C Deriving ARDL Lag Weights • Appendix 9D Forecasting: Exponential Smoothing Principles of Econometrics, 3rd Edition

  46. Appendix 9A Generalized Least Squares Estimation Principles of Econometrics, 3rd Edition

  47. Appendix 9A Generalized Least Squares Estimation Principles of Econometrics, 3rd Edition

  48. Appendix 9A Generalized Least Squares Estimation Principles of Econometrics, 3rd Edition

  49. Appendix 9A Generalized Least Squares Estimation Principles of Econometrics, 3rd Edition

  50. Appendix 9B The Durbin-Watson Test Principles of Econometrics, 3rd Edition

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