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Density Forecast Evaluation in Unstable Environments

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  • Gloria Gonzalez-Rivera

    () (Department of Economics, University of California Riverside)

  • Yingying Sun

Abstract

We propose a density forecast evaluation method in the presence of instabilities, which are defined as breaks in any conditional moment of interest and/or in the functional form of the conditional density of the process. Within the framework of the autocontour-based tests proposed by González-Rivera et al. (2011) and González-Rivera and Sun (2015), we construct Sup- and Ave-type tests, calculated over a collection of subsamples in the evaluation period. These tests have asymptotic distributions that are nuisance-parameter free and they are correctly sized and very powerful for detecting breaks in the parameters of the conditional mean and conditional variance. A power comparison with the tests of Rossi and Sekhposyan (2013) shows that our tests are more powerful across the models considered in their work. We analyze the stability of a dynamic Phillips curve and find that the best one-step-ahead density forecast of changes in inflation is generated by a Markov switching model that allows state shifts in the mean and variance of inflation changes as well as in the coefficient that links inflation and unemployment.
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Suggested Citation

  • Gloria Gonzalez-Rivera & Yingying Sun, 2014. "Density Forecast Evaluation in Unstable Environments," Working Papers 201428, University of California at Riverside, Department of Economics.
  • Handle: RePEc:ucr:wpaper:201428
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    File URL: https://economics.ucr.edu/repec/ucr/wpaper/201428.pdf
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    References listed on IDEAS

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    1. Kenneth S. Rogoff & Vania Stavrakeva, 2008. "The Continuing Puzzle of Short Horizon Exchange Rate Forecasting," NBER Working Papers 14071, National Bureau of Economic Research, Inc.
    2. Rossi, Barbara, 2006. "Are Exchange Rates Really Random Walks? Some Evidence Robust To Parameter Instability," Macroeconomic Dynamics, Cambridge University Press, vol. 10(01), pages 20-38, February.
    3. Paye, Bradley S. & Timmermann, Allan, 2006. "Instability of return prediction models," Journal of Empirical Finance, Elsevier, vol. 13(3), pages 274-315, June.
    4. González-Rivera, Gloria & Senyuz, Zeynep & Yoldas, Emre, 2011. "Autocontours: Dynamic Specification Testing," Journal of Business & Economic Statistics, American Statistical Association, vol. 29(1), pages 186-200.
    5. Rossi, Barbara & Sekhposyan, Tatevik, 2010. "Have economic models' forecasting performance for US output growth and inflation changed over time, and when?," International Journal of Forecasting, Elsevier, vol. 26(4), pages 808-835, October.
    6. Hansen, Bruce E., 2000. "Testing for structural change in conditional models," Journal of Econometrics, Elsevier, vol. 97(1), pages 93-115, July.
    7. Barbara Rossi & Tatevik Sekhposyan, 2011. "Forecast Optimality Tests in the Presence of Instabilities," Working Papers 11-18, Duke University, Department of Economics.
    8. Andrews, Donald W K & Ploberger, Werner, 1994. "Optimal Tests When a Nuisance Parameter Is Present Only under the Alternative," Econometrica, Econometric Society, vol. 62(6), pages 1383-1414, November.
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    10. Amit Goyal & Ivo Welch, 2003. "Predicting the Equity Premium with Dividend Ratios," Management Science, INFORMS, vol. 49(5), pages 639-654, May.
    11. Rossi, Barbara & Sekhposyan, Tatevik, 2013. "Conditional predictive density evaluation in the presence of instabilities," Journal of Econometrics, Elsevier, vol. 177(2), pages 199-212.
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    17. González-Rivera, Gloria & Yoldas, Emre, 2012. "Autocontour-based evaluation of multivariate predictive densities," International Journal of Forecasting, Elsevier, vol. 28(2), pages 328-342.
    18. Amisano, Gianni & Giacomini, Raffaella, 2007. "Comparing Density Forecasts via Weighted Likelihood Ratio Tests," Journal of Business & Economic Statistics, American Statistical Association, vol. 25, pages 177-190, April.
    19. James H. Stock & Mark W.Watson, 2003. "Forecasting Output and Inflation: The Role of Asset Prices," Journal of Economic Literature, American Economic Association, vol. 41(3), pages 788-829, September.
    20. Valentina Corradi & Norman Swanson, 2006. "Predictive Density Evaluation. Revised," Departmental Working Papers 200621, Rutgers University, Department of Economics.
    21. Corradi, Valentina & Swanson, Norman R., 2006. "Predictive Density Evaluation," Handbook of Economic Forecasting, Elsevier.
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    Cited by:

    1. Emilio Zanetti Chini, 0201. "Forecaster’s utility and forecasts coherence," CREATES Research Papers 2018-01, Department of Economics and Business Economics, Aarhus University.

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