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Nonparametric Bootstrap Procedures for Predictive Inference Based on Recursive Estimation Schemes

  • Norman Swanson

    ()

    (Rutgers University)

  • Valentina Corradi

    ()

    (Queen Mary, University of London)

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 examples where predictive accuracy tests are made operational using our new bootstrap procedures. In one application, we outline a consistent test for out-of-sample nonlinear Granger causality, and in the other we outline a test for selecting amongst multiple alternative forecasting models, all of which are possibly misspecified. More specifically, our examples extend the White (2000) reality check to the case of non vanishing parameter estimation error, and extend the integrated conditional moment tests of Bierens (1982, 1990) and Bierens and Ploberger (1997) to the case of out-of-sample prediction. In both examples, appropriate re-centering of the bootstrap score is required in order to ensure that the tests have asymptotically correct size, and the need for such re-centering is shown to arise quite naturally when testing hypotheses of predictive accuracy. In a Monte Carlo investigation, we compare the finite sample properties of our block bootstrap procedures with the parametric bootstrap due to Kilian (1999); all within the context of various encompassing and predictive accuracy tests. An empirical illustration is also discussed, in which it is found that unemployment appears to have nonlinear marginal predictive content for inflation.

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Paper provided by Rutgers University, Department of Economics in its series Departmental Working Papers with number 200618.

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Length: 20 pages
Date of creation: 22 Sep 2006
Date of revision:
Handle: RePEc:rut:rutres:200618
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  1. Kilian, Lutz & Taylor, Mark P., 2003. "Why is it so difficult to beat the random walk forecast of exchange rates?," Journal of International Economics, Elsevier, vol. 60(1), pages 85-107, May.
  2. Todd E. Clark & Michael McCracken, 1999. "Tests of Equal Forecast Accuracy and Encompassing for Nested Models," Computing in Economics and Finance 1999 1241, Society for Computational Economics.
  3. 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.
  4. Inoue, Atsushi & Rossi, Barbara, 2005. "Recursive Predictability Tests for Real-Time Data," Journal of Business & Economic Statistics, American Statistical Association, vol. 23, pages 336-345, July.
  5. Goncalves, Silvia & White, Halbert, 2000. "Maximum Likelihood and the Bootstrap for Nonlinear Dynamic Models," University of California at San Diego, Economics Working Paper Series qt1bj657ff, Department of Economics, UC San Diego.
  6. McCracken, Michael W & Sapp, Stephen G, 2005. "Evaluating the Predictability of Exchange Rates Using Long-Horizon Regressions: Mind Your p's and q's!," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 37(3), pages 473-94, June.
  7. 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.
  8. Bierens, H.J. & Ploberger, W., 1995. "Asymptotic theory of integrated conditional moment tests," Discussion Paper 1995-124, Tilburg University, Center for Economic Research.
  9. Todd E. Clark & Michael W. McCracken, 2001. "Evaluating long-horizon forecasts," Research Working Paper RWP 01-14, Federal Reserve Bank of Kansas City.
  10. Kenneth D. West, 1994. "Asymptotic Inference About Predictive Ability," Macroeconomics 9410002, EconWPA.
  11. Inoue, Atsushi & Kilian, Lutz, 2003. "On the selection of forecasting models," Working Paper Series 0214, European Central Bank.
  12. Newey, Whitney & West, Kenneth, 2014. "A simple, positive semi-definite, heteroscedasticity and autocorrelation consistent covariance matrix," Applied Econometrics, Publishing House "SINERGIA PRESS", vol. 33(1), pages 125-132.
  13. Elliott, Graham & Timmermann, Allan, 2002. "Optimal Forecast Combination Under General Loss Functions and Forecast Error Distributions," University of California at San Diego, Economics Working Paper Series qt15r9t2q2, Department of Economics, UC San Diego.
  14. 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.
  15. Christoffersen, Peter F. & Diebold, Francis X., 1997. "Optimal Prediction Under Asymmetric Loss," Econometric Theory, Cambridge University Press, vol. 13(06), pages 808-817, December.
  16. Donald W.K. Andrews, 1999. "Higher-Order Improvements of a Computationally Attractive-Step Bootstrap for Extremum Estimators," Cowles Foundation Discussion Papers 1230, Cowles Foundation for Research in Economics, Yale University.
  17. Inoue, Atsushi, 2001. "Testing For Distributional Change In Time Series," Econometric Theory, Cambridge University Press, vol. 17(01), pages 156-187, February.
  18. 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.
  19. Corradi, Valentina & Swanson, Norman R., 2004. "Some recent developments in predictive accuracy testing with nested models and (generic) nonlinear alternatives," International Journal of Forecasting, Elsevier, vol. 20(2), pages 185-199.
  20. Clive W.J. Granger, 1999. "Outline of forecast theory using generalized cost functions," Spanish Economic Review, Springer, vol. 1(2), pages 161-173.
  21. repec:cup:macdyn:v:5:y:2001:i:4:p:598-620 is not listed on IDEAS
  22. Corradi, Valentina, 1999. "Deciding Between I(0) And I(1) Via Flil-Based Bounds," Econometric Theory, Cambridge University Press, vol. 15(05), pages 643-663, October.
  23. Graham Elliott & Allan Timmermann, 2008. "Economic Forecasting," Journal of Economic Literature, American Economic Association, vol. 46(1), pages 3-56, March.
  24. 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.
  25. Swanson, N.R. & White, H., 1995. "A Models Selection Approach to Real-Time Macroeconomic Forecasting Using Linear Models and Artificial Neural Networks," Papers 04-95-12, Pennsylvania State - Department of Economics.
  26. Corradi, V. & Swanson, N.R., 2000. "A Consistent Test for Nonlinear Out of Sample Predictive Accuracy," Discussion Papers 0012, Exeter University, Department of Economics.
  27. Halbert White, 2000. "A Reality Check for Data Snooping," Econometrica, Econometric Society, vol. 68(5), pages 1097-1126, September.
  28. Inoue, Atsushi & Shintani, Mototsugu, 2006. "Bootstrapping GMM estimators for time series," Journal of Econometrics, Elsevier, vol. 133(2), pages 531-555, August.
  29. Wooldridge, Jeffrey M. & White, Halbert, 1988. "Some Invariance Principles and Central Limit Theorems for Dependent Heterogeneous Processes," Econometric Theory, Cambridge University Press, vol. 4(02), pages 210-230, August.
  30. Hansen, B.E., 1991. "Inference when a Nuisance Parameter is Not Identified Under the Null Hypothesis," RCER Working Papers 296, University of Rochester - Center for Economic Research (RCER).
  31. Schorfheide, Frank, 2005. "VAR forecasting under misspecification," Journal of Econometrics, Elsevier, vol. 128(1), pages 99-136, September.
  32. Kilian, Lutz, 1999. "Exchange Rates and Monetary Fundamentals: What Do We Learn from Long-Horizon Regressions?," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 14(5), pages 491-510, Sept.-Oct.
  33. 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.
  34. McCracken, Michael W., 2007. "Asymptotics for out of sample tests of Granger causality," Journal of Econometrics, Elsevier, vol. 140(2), pages 719-752, October.
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