Dynamic models autocorrelation and forecasting
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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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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

  • 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


    9.1 Introduction

    Figure 9.1

    Principles of Econometrics, 3rd Edition


    9.1 Introduction

    Principles of Econometrics, 3rd Edition


    9.1 Introduction

    Figure 9.2(a) Time Series of a Stationary Variable

    Principles of Econometrics, 3rd Edition


    9.1 Introduction

    Figure 9.2(b) Time Series of a Nonstationary Variable that is ‘Slow Turning’ or ‘Wandering’

    Principles of Econometrics, 3rd Edition


    9.1 Introduction

    Figure 9.2(c) Time Series of a Nonstationary Variable that ‘Trends’

    Principles of Econometrics, 3rd Edition


    9.2 Lags in the Error Term: Autocorrelation

    9.2.1 Area Response Model for Sugar Cane

    Principles of Econometrics, 3rd Edition


    9.2.2 First-Order Autoregressive Errors

    Principles of Econometrics, 3rd Edition


    9.2.2 First-Order Autoregressive Errors

    Principles of Econometrics, 3rd Edition


    9.2.2 First-Order Autoregressive Errors

    Principles of Econometrics, 3rd Edition


    9.2.2 First-Order Autoregressive Errors

    Principles of Econometrics, 3rd Edition


    9.2.2 First-Order Autoregressive Errors

    Figure 9.3 Least Squares Residuals Plotted Against Time

    Principles of Econometrics, 3rd Edition


    9.2.2 First-Order Autoregressive Errors

    Principles of Econometrics, 3rd Edition


    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


    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


    9.3.2 Nonlinear Least Squares Estimation

    Principles of Econometrics, 3rd Edition


    9.3.2 Nonlinear Least Squares Estimation

    Principles of Econometrics, 3rd Edition


    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


    9.3.3 Estimating a More General Model

    Principles of Econometrics, 3rd Edition


    9.4Testing for Autocorrelation

    9.4.1Residual Correlogram

    Principles of Econometrics, 3rd Edition


    9.4Testing for Autocorrelation

    9.4.1Residual Correlogram

    Principles of Econometrics, 3rd Edition


    9.4.1 Residual Correlogram

    Figure 9.4 Correlogram for Least Squares Residuals from Sugar Cane Example

    Principles of Econometrics, 3rd Edition


    9.4.1 Residual Correlogram

    Principles of Econometrics, 3rd Edition


    9.4.1 Residual Correlogram

    Figure 9.5 Correlogram for Nonlinear Least Squares Residualsfrom Sugar Cane Example

    Principles of Econometrics, 3rd Edition


    9.4.2 A Lagrange Multiplier Test

    Principles of Econometrics, 3rd Edition


    9.4.2 A Lagrange Multiplier Test

    Principles of Econometrics, 3rd Edition


    9.5 An Introduction to Forecasting: Autoregressive Models

    Principles of Econometrics, 3rd Edition


    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


    9.5 An Introduction to Forecasting: Autoregressive Models

    Principles of Econometrics, 3rd Edition


    9.5 An Introduction to Forecasting: Autoregressive Models

    Principles of Econometrics, 3rd Edition


    9.5 An Introduction to Forecasting: Autoregressive Models

    Principles of Econometrics, 3rd Edition


    9.5 An Introduction to Forecasting: Autoregressive Models

    Principles of Econometrics, 3rd Edition


    9.5 An Introduction to Forecasting: Autoregressive Models

    Principles of Econometrics, 3rd Edition


    9.6 Finite Distributed Lags

    Principles of Econometrics, 3rd Edition


    9.6 Finite Distributed Lags

    Principles of Econometrics, 3rd Edition


    9.6 Finite Distributed Lags

    Principles of Econometrics, 3rd Edition


    9.7Autoregressive Distributed Lag Models

    Principles of Econometrics, 3rd Edition


    9.7Autoregressive Distributed Lag Models

    Figure 9.7 Correlogram for Least Squares Residuals fromFinite Distributed Lag Model

    Principles of Econometrics, 3rd Edition


    9.7Autoregressive Distributed Lag Models

    Principles of Econometrics, 3rd Edition


    9.7Autoregressive Distributed Lag Models

    Figure 9.8 Correlogram for Least Squares Residuals from Autoregressive Distributed Lag Model

    Principles of Econometrics, 3rd Edition


    9.7Autoregressive Distributed Lag Models

    Principles of Econometrics, 3rd Edition


    9.7Autoregressive Distributed Lag Models

    Figure 9.9 Distributed Lag Weights for Autoregressive Distributed Lag Model

    Principles of Econometrics, 3rd Edition


    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


    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


    Appendix 9A Generalized Least Squares Estimation

    Principles of Econometrics, 3rd Edition


    Appendix 9A Generalized Least Squares Estimation

    Principles of Econometrics, 3rd Edition


    Appendix 9A Generalized Least Squares Estimation

    Principles of Econometrics, 3rd Edition


    Appendix 9A Generalized Least Squares Estimation

    Principles of Econometrics, 3rd Edition


    Appendix 9B The Durbin-Watson Test

    Principles of Econometrics, 3rd Edition


    Appendix 9B The Durbin-Watson Test

    Principles of Econometrics, 3rd Edition


    Appendix 9B The Durbin-Watson Test

    Principles of Econometrics, 3rd Edition


    Appendix 9B The Durbin-Watson Test

    Figure 9A.1:

    Principles of Econometrics, 3rd Edition


    Appendix 9B 9B.1 The Durbin-Watson Bounds Test

    Figure 9A.2:

    Principles of Econometrics, 3rd Edition


    Appendix 9B 9B.1 The Durbin-Watson Bounds Test

    The Durbin-Watson bounds test.

    • if the test is inconclusive.

    Principles of Econometrics, 3rd Edition


    Appendix 9C Deriving ARDL Lag Weights

    Principles of Econometrics, 3rd Edition


    Appendix 9C 9C.1 The Geometric Lag

    Principles of Econometrics, 3rd Edition


    Appendix 9C 9C.1 The Geometric Lag

    Principles of Econometrics, 3rd Edition


    Appendix 9C 9C.1 The Geometric Lag

    Principles of Econometrics, 3rd Edition


    Appendix 9C 9C.1 The Geometric Lag

    Principles of Econometrics, 3rd Edition


    Appendix 9C 9C.2 Lag Weights for More General ARDL Models

    Principles of Econometrics, 3rd Edition


    Appendix 9D Forecasting: Exponential Smoothing

    Principles of Econometrics, 3rd Edition


    Appendix 9D Forecasting: Exponential Smoothing

    Figure 9A.3: Exponential Smoothing Forecasts for two alternative values of α

    Principles of Econometrics, 3rd Edition


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