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A predictability test for a small number of nested models

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

Abstract

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: B23, C53

Suggested Citation

  • Hubrich, Kirstin & Granziera, Eleonora & Moon, Hyungsik Roger, 2013. "A predictability test for a small number of nested models," Working Paper Series 1580, European Central Bank.
  • Handle: RePEc:ecb:ecbwps:20131580
    Note: 1325881
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    References listed on IDEAS

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    Cited by:

    1. Granziera, Eleonora & Sekhposyan, Tatevik, 2019. "Predicting relative forecasting performance: An empirical investigation," International Journal of Forecasting, Elsevier, vol. 35(4), pages 1636-1657.
    2. Clark, Todd & McCracken, Michael, 2013. "Advances in Forecast Evaluation," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 2, chapter 0, pages 1107-1201, Elsevier.
    3. Kirstin Hubrich & Frauke Skudelny, 2017. "Forecast Combination for Euro Area Inflation: A Cure in Times of Crisis?," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 36(5), pages 515-540, August.
    4. Daniel Borup & Martin Thyrsgaard, 2017. "Statistical tests for equal predictive ability across multiple forecasting methods," CREATES Research Papers 2017-19, Department of Economics and Business Economics, Aarhus University.
    5. Dichtl, Hubert & Drobetz, Wolfgang & Neuhierl, Andreas & Wendt, Viktoria-Sophie, 2021. "Data snooping in equity premium prediction," International Journal of Forecasting, Elsevier, vol. 37(1), pages 72-94.

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    More about this item

    Keywords

    direct multi-step forecasts; fixed regressors bootstrap; multi-model comparison; out-of sample; point-forecast evaluation; predictive ability;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods

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