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Bootstrap Procedures for Recursive Estimation Schemes With Applications to Forecast Model Selection

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Author Info

  • Valentina Corradi

    ()
    (Queen Mary, University of London)

  • Norman Swanson

    ()
    (Rutgers University)

Abstract

In recent years it has become apparent that many of the classical testing procedures used to select amongst alternative economic theories and economic models are not realistic. In particular, researchers have become more aware of the fact that parameter estimation error and data dependence play a crucial role in test statistic limiting distributions, a role which had hitherto been ignored to a large extent. Given the fact that one of the primary ways for comparing di®erent models and theories is via use of predictive accuracy tests, it is perhaps not surprising that a large literature on the topic has developed over the last 10 years, including, for example, important papers by Diebold and Mariano (1995), West (1996), and White (2000). In this literature, it is quite common to compare multiple models (which are possibly all misspeci¯ed - i.e. they are all approximations of some unknown true model) in terms of their out of sample predictive ability, for given loss function. Our objectives in this paper are twofold. First, we introduce block bootstrap techniques that are (first order) valid in recursive estimation frameworks. Thereafter, we present two applications where predictive accuracy tests are made operational using our new bootstrap procedures. One of the applications outlines a consistent test for out-of-sample nonlinear Granger causality, and the other outlines a test for selecting amongst multiple alternative forecasting models, all of which may be viewed as approximations of some unknown underlying model. More speci¯cally, our examples extend the White (2000) reality check to the case of non vanishing parameter estimation error, and extend the integrated conditional moment (ICM) tests of Bierens (1982, 1990) and Bierens and Ploberger (1997) to the case of out-of-sample prediction. Of note is that in both of these examples, it is shown that appropriate re-centering of the bootstrap score is required in order to ensure that the tests are properly sized, and the need for such re-centering is shown to arise quite naturally when testing hypotheses of predictive accuracy. The results of a Monte Carlo investigation of the ICM test suggest that the bootstrap procedure proposed in this paper yield tests with reasonable ¯nite sample properties for samples with as few as 300 observations.

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Bibliographic Info

Paper provided by Rutgers University, Department of Economics in its series Departmental Working Papers with number 200418.

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Length: 20 pages
Date of creation: 16 Sep 2004
Date of revision:
Handle: RePEc:rut:rutres:200418

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Keywords: Predictive density;

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References

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  1. Christoffersen & Diebold, . "Optimal Prediction Under Asymmetric Loss," Home Pages 167, 1996., University of Pennsylvania.
  2. Linton, Oliver & Maasoumi, Esfandiar & Whang, Yoon-Jae, 2003. "Consistent Testing for Stochastic Dominance under General Sampling Schemes," SFB 373 Discussion Papers 2003,31, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
  3. Francis X. Diebold & Celia Chen, 1993. "Testing structural stability with endogenous break point: a size comparison of analytic and bootstrap procedures," Working Papers 93-11, Federal Reserve Bank of Philadelphia.
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  5. Goncalves, Silvia & White, Halbert, 2004. "Maximum likelihood and the bootstrap for nonlinear dynamic models," Journal of Econometrics, Elsevier, vol. 119(1), pages 199-219, March.
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  7. Filippo Altissimo & Valentina Corradi, 2002. "Bounds for inference with nuisance parameters present only under the alternative," Econometrics Journal, Royal Economic Society, vol. 5(2), pages 494-519, 06.
  8. Graham Elliott & Allan Timmermann, 2005. "Optimal Forecast Combination Under Regime Switching ," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 46(4), pages 1081-1102, November.
  9. Valentina Corradi & Norman Swanson, 2003. "Some Recent Developments in Predictive Accuracy Testing With Nested Models and (Generic) Nonlinear Alternatives," Departmental Working Papers 200316, Rutgers University, Department of Economics.
  10. Halbert White, 2000. "A Reality Check for Data Snooping," Econometrica, Econometric Society, vol. 68(5), pages 1097-1126, September.
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  12. Norman R. Swanson & Halbert White, 1997. "A Model Selection Approach To Real-Time Macroeconomic Forecasting Using Linear Models And Artificial Neural Networks," The Review of Economics and Statistics, MIT Press, vol. 79(4), pages 540-550, November.
  13. Valentina Corradi & Norman Swanson, 2004. "Predictive Density Evaluation," Departmental Working Papers 200419, Rutgers University, Department of Economics.
  14. Newey, Whitney K & West, Kenneth D, 1987. "A Simple, Positive Semi-definite, Heteroskedasticity and Autocorrelation Consistent Covariance Matrix," Econometrica, Econometric Society, vol. 55(3), pages 703-08, May.
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  24. Christoffersen & Diebold, . "Further Results on Forecasting and Model Selection Under Asymmetric Loss," Home Pages _059, University of Pennsylvania.
  25. Schorfheide, Frank, 2005. "VAR forecasting under misspecification," Journal of Econometrics, Elsevier, vol. 128(1), pages 99-136, September.
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  27. Norman R. Swanson, 2000. "An Out of Sample Test for Granger Causality," Econometric Society World Congress 2000 Contributed Papers 0362, Econometric Society.
  28. Weiss, Andrew A, 1996. "Estimating Time Series Models Using the Relevant Cost Function," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 11(5), pages 539-60, Sept.-Oct.
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  30. Elliott, Graham & Timmermann, Allan, 2004. "Optimal forecast combinations under general loss functions and forecast error distributions," Journal of Econometrics, Elsevier, vol. 122(1), pages 47-79, September.
  31. Hall, Peter & Horowitz, Joel L, 1996. "Bootstrap Critical Values for Tests Based on Generalized-Method-of-Moments Estimators," Econometrica, Econometric Society, vol. 64(4), pages 891-916, July.
  32. Stinchcombe, Maxwell B. & White, Halbert, 1998. "Consistent Specification Testing With Nuisance Parameters Present Only Under The Alternative," Econometric Theory, Cambridge University Press, vol. 14(03), pages 295-325, June.
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Cited by:
  1. Valentina Corradi & Norman Swanson, 2004. "Predective Density and Conditional Confidence Interval Accuracy Tests," Departmental Working Papers 200423, Rutgers University, Department of Economics.

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