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Density forecast evaluation in unstable environments

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  • González-Rivera, Gloria
  • Sun, Yingying

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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  • González-Rivera, Gloria & Sun, Yingying, 2017. "Density forecast evaluation in unstable environments," International Journal of Forecasting, Elsevier, vol. 33(2), pages 416-432.
    • Handle: RePEc:eee:intfor:v:33:y:2017:i:2:p:416-432
    DOI: 10.1016/j.ijforecast.2016.10.003
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. Elliott, Graham & Muller, Ulrich K., 2007. "Confidence sets for the date of a single break in linear time series regressions," Journal of Econometrics, Elsevier, vol. 141(2), pages 1196-1218, December.
    4. Rossi, Barbara & Sekhposyan, Tatevik, 2013. "Conditional predictive density evaluation in the presence of instabilities," Journal of Econometrics, Elsevier, vol. 177(2), pages 199-212.
    5. Stock, James H. & Watson, Mark W., 1999. "Forecasting inflation," Journal of Monetary Economics, Elsevier, vol. 44(2), pages 293-335, October.
    6. Pesaran, M. Hashem & Timmermann, Allan, 2002. "Market timing and return prediction under model instability," Journal of Empirical Finance, Elsevier, vol. 9(5), pages 495-510, December.
    7. González-Rivera, Gloria & Sun, Yingying, 2015. "Generalized autocontours: Evaluation of multivariate density models," International Journal of Forecasting, Elsevier, vol. 31(3), pages 799-814.
    8. Diebold, Francis X & Gunther, Todd A & Tay, Anthony S, 1998. "Evaluating Density Forecasts with Applications to Financial Risk Management," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 863-883, November.
    9. González-Rivera, Gloria & Yoldas, Emre, 2012. "Autocontour-based evaluation of multivariate predictive densities," International Journal of Forecasting, Elsevier, vol. 28(2), pages 328-342.
    10. 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.
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    19. Hansen, Bruce E., 2000. "Testing for structural change in conditional models," Journal of Econometrics, Elsevier, vol. 97(1), pages 93-115, July.
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    Cited by:

    1. Emilio Zanetti Chini, 2018. "Forecaster’s utility and forecasts coherence," DEM Working Papers Series 145, University of Pavia, Department of Economics and Management.

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