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Combining Tests of Predictive Ability Theory and Evidence for Chilean and Canadian Exchange Rates

  • Pablo Pincheira

In this paper we focus on combining out-of-sample test statistics of the Martingale Difference Hypothesis (MDH) to explore whether a new combined statistic may induce a test with higher asymptotic power. Asymptotic normality implies that more power can be achieved by finding the optimal weight in a combined t-ratio. Unfortunately, this optimal weight is degenerated under the null of no predictability. To overcome this problem we introduce a penalization function that attracts the optimal weight to the interior of the feasible combination set. The new optimal weight associated with the penalization problem is well defined under the null, ensuring asymptotic normality of the resulting combined test. We show, via simulations, that our proposed combined test displays important gains in power and good empirical size. In fact, the new test outperforms its single components displaying gains in power up to 45%. Finally, we illustrate our approach with an empirical application aimed at testing predictability of Chilean and Canadian exchange rate returns.

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Paper provided by Central Bank of Chile in its series Working Papers Central Bank of Chile with number 459.

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Date of creation: Feb 2008
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Handle: RePEc:chb:bcchwp:459
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  1. Inoue, Atsushi & Kilian, Lutz, 2002. "In-Sample or Out-of-Sample Tests of Predictability: Which One Should We Use?," CEPR Discussion Papers 3671, C.E.P.R. Discussion Papers.
  2. McCracken,M.W. & West,K.D., 2001. "Inference about predictive ability," Working papers 14, Wisconsin Madison - Social Systems.
  3. Todd Clark & Michael McCracken, 2005. "Evaluating Direct Multistep Forecasts," Econometric Reviews, Taylor & Francis Journals, vol. 24(4), pages 369-404.
  4. Cheung, Yin-Wong & Chinn, Menzie David & Garcia Pascual, Antonio, 2003. "Empirical Exchange Rate Models of the Nineties: Are Any Fit to Survive?," Santa Cruz Department of Economics, Working Paper Series qt12z9x4c5, Department of Economics, UC Santa Cruz.
  5. McCracken, Michael W., 2007. "Asymptotics for out of sample tests of Granger causality," Journal of Econometrics, Elsevier, vol. 140(2), pages 719-752, October.
  6. Pablo Pincheira, 2006. "Shrinkage Based Tests of the Martingale Difference Hypothesis," Working Papers Central Bank of Chile 376, Central Bank of Chile.
  7. David Hendry & Michael Clements, 2001. "Pooling of Forecasts," Economics Series Working Papers 2002-W09, University of Oxford, Department of Economics.
  8. Diebold, Francis X & Mariano, Roberto S, 1995. "Comparing Predictive Accuracy," Journal of Business & Economic Statistics, American Statistical Association, vol. 13(3), pages 253-63, July.
  9. Kenneth D. West & Todd Clark, 2006. "Approximately Normal Tests for Equal Predictive Accuracy in Nested Models," NBER Technical Working Papers 0326, National Bureau of Economic Research, Inc.
  10. Meese, Richard A. & Rogoff, Kenneth, 1983. "Empirical exchange rate models of the seventies : Do they fit out of sample?," Journal of International Economics, Elsevier, vol. 14(1-2), pages 3-24, February.
  11. Anatolyev, Stanislav & Gerko, Alexander, 2005. "A Trading Approach to Testing for Predictability," Journal of Business & Economic Statistics, American Statistical Association, vol. 23, pages 455-461, October.
  12. Avramov, Doron, 2002. "Stock return predictability and model uncertainty," Journal of Financial Economics, Elsevier, vol. 64(3), pages 423-458, June.
  13. Donald J. Brown & Rustam Ibragimov, 2005. "Sign Tests for Dependent Observations and Bounds for Path-Dependent Options," Cowles Foundation Discussion Papers 1518, Cowles Foundation for Research in Economics, Yale University.
  14. Clemen, Robert T., 1989. "Combining forecasts: A review and annotated bibliography," International Journal of Forecasting, Elsevier, vol. 5(4), pages 559-583.
  15. Norman R. Swanson, 2000. "An Out of Sample Test for Granger Causality," Econometric Society World Congress 2000 Contributed Papers 0362, Econometric Society.
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