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A predictability test for a small number of nested models

  • Granziera, Eleonora
  • Hubrich, Kirstin
  • Moon, Hyungsik Roger

In this paper we introduce Quasi Likelihood Ratio tests for one sided multivariate hypotheses to evaluate the null that a parsimonious model performs equally well as a small number of models which nest the benchmark. We show that the limiting distributions of the test statistics are non standard. For critical values we consider two approaches: (i) bootstrapping and (ii) simulations assuming normality of the mean square prediction error (MSPE) difference. The size and the power performance of the tests are compared via Monte Carlo experiments with existing equal and superior predictive ability tests for multiple model comparison. We find that our proposed tests are well sized for one step ahead as well as for multi-step ahead forecasts when critical values are bootstrapped. The experiments on the power reveal that the superior predictive ability test performs last while the ranking between the quasi likelihood-ratio test and the other equal predictive ability tests depends on the simulation settings. Last, we apply our test to draw conclusions about the predictive ability of a Phillips type curve for the US core inflation. JEL Classification:

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Paper provided by European Central Bank in its series Working Paper Series with number 1580.

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Date of creation: Aug 2013
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Handle: RePEc:ecb:ecbwps:20131580
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  1. Francesco Ravazzolo & Philip Rothman, 2011. "Oil and US GDP: A Real-Time out-of Sample Examination," Working Papers 0004, Centre for Applied Macro- and Petroleum economics (CAMP), BI Norwegian Business School.
  2. Hansen, Peter Reinhard, 2005. "A Test for Superior Predictive Ability," Journal of Business & Economic Statistics, American Statistical Association, vol. 23, pages 365-380, October.
  3. West, Kenneth D, 1996. "Asymptotic Inference about Predictive Ability," Econometrica, Econometric Society, vol. 64(5), pages 1067-84, September.
  4. Clark, Todd E. & West, Kenneth D., 2007. "Approximately normal tests for equal predictive accuracy in nested models," Journal of Econometrics, Elsevier, vol. 138(1), pages 291-311, May.
  5. Corradi, Valentina & Swanson, Norman R., 2002. "A consistent test for nonlinear out of sample predictive accuracy," Journal of Econometrics, Elsevier, vol. 110(2), pages 353-381, October.
  6. White, Halbert, 1982. "Maximum Likelihood Estimation of Misspecified Models," Econometrica, Econometric Society, vol. 50(1), pages 1-25, January.
  7. Halbert White, 2000. "A Reality Check for Data Snooping," Econometrica, Econometric Society, vol. 68(5), pages 1097-1126, September.
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