Nonstationary Time Series Analysis and Cointegration

By Colin P. Hargreaves | Go to book overview

2 Towards a theory of economic forecasting

Michael P. Clements and David F. Hendry*

Some recent developments in the theory of economic forecasting using econometric systems are reviewed. Measures of forecast uncertainty for conditional and unconditional forecasts suggest a limit to forecastability and show the potential advantages of combining types of forecast to improve accuracy; but pooling forecasts from rival econometric models violates encompassing. Mean square forecast error comparisons are criticized in favour of generalized forecast error second moments: only the latter are invariant to linear transformations. We delineate five sources of forecast uncertainty: parameter non-constancy; estimation uncertainty; variable uncertainty; innovation uncertainty; and model misspecification. A theory of intercept corrections to mitigate such errors is discussed. Asymptotic forecast error variance formulae for nonstationary economic time series depend on the treatment of unit roots and cointegration but work well in finite samples, and show that forecast evaluation based on differenced data may fail to reveal inadequate models.


1. INTRODUCTION

We consider several aspects of the theory of economic forecasting based on econometric models. The term forecast is used to denote a statement about a future event or set of events; prediction is used to denote an implication of a model, so forecasts are a sub-class of predictions. We do not assume that the data generation process (DGP) is constant over time or that the model coincides with that DGP,

____________________
*
Financial support from the U.K. Economic and Social Research Council under grant R000233447 is gratefully acknowledged by both authors. We are indebted to Nell Ericsson for helpful comments.

-9-

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Nonstationary Time Series Analysis and Cointegration
Table of contents

Table of contents

  • Title Page iii
  • Contents v
  • List of Figures vii
  • List of Tables xiii
  • List of Contributors xv
  • Foreword xvii
  • 1 - Introduction 1
  • References 8
  • 2 - Towards a Theory of Economic Forecasting 9
  • Appendix 48
  • References 50
  • 3 - Bayes Models and Forecasts of Australian Macroeconomic Time Series 53
  • References 86
  • 4 - A Review of Methods of Estimating Cointegrating Relationships 87
  • References 129
  • 5 - A Test of the Null Hypothesis of Cointegration 133
  • References 151
  • 6 - Modelling Seasonal Variation 153
  • References 176
  • 7 - Cointegration, Seasonality, Encompassing, and the Demand for Money in the Uk 179
  • Appendix A. the Data 214
  • Appendix B. Sequential Reduction Analysis 216
  • References 220
  • 8 - Evaluating a Real Business Cycle Model 225
  • Appendix 252
  • References 254
  • 9 - Misspecification Versus Bubbles in the Cagan Hyperinflation Model 257
  • References 281
  • 10 Regime Switching with Time-Varying Transition Probabilities 283
  • Appendix 299
  • References 302
  • Name Index 303
  • Subject Index 307
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