# Nonstationary Time Series Analysis and Cointegration

By Colin P. Hargreaves | Go to book overview

1993b). In any case, selecting the model with the minimum MSFE is an inadequate strategy since the model need not have constant parameters, nor encompass the forecast errors of competing models.

There appears to be a relatively short forecast horizon over which econometric models can yield marked gains relative to unconditional forecasts. This problem is exacerbated by the potential non-monotonicity of forecast variances as the horizon increases. We reconsidered the benefits of pooling complementary sources of forecast information, as against the weaknesses inherent in pooling forecasts based on competing models, which are implicit encompassing tests. We evaluated the role of intercept corrections, drawing on a recent taxonomy to demonstrate that specific forms of such corrections can make forecasts more robust to model misspecification and to structural change. This finding is consistent with the empirical evidence that intercept corrections improve model-based forecasts.

A comprehensive list of sources of forecast error was developed, and a positive aspect of our paper was to reveal where econometrics could contribute value added to the forecasting process in a world where models are mimics rather than facsimiles of the data generation process, where that process is not constant over time, and where investigators disagree about model choice.

APPENDIX

We use three approximations to obtain a more tractable expression following Schmidt ( 1977), Baillie ( 1979b) and Chong and Hendry ( 1986). Let:
ψ + ̂ = ψ + δ (101) where δ is Op(1/√T) so that powers of δ are asymptotically negligible, then:
ψ + ̂h= (ψ + δ)h ≅ ψh + hδψh-1 = ψh + hψh-1(ψ + ̂ - ψ). (102) Consequently:
V[ψ + ̂h - ψh] ≅ V[hψh-1(ψ + ̂ - ψ)] = h2ψ2(h-1)V[ψ + ̂]. (103) This result also follows from the usual formula for a nonlinear estimation function:

. (104) Next:

-48-

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Nonstationary Time Series Analysis and Cointegration

• 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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