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Elicitability and Encompassing for Volatility Forecasts by Bregman Functions

Author

Listed:
  • Tae-Hwy Lee

    (Department of Economics, University of California Riverside)

  • Ekaterina Seregina

    (Colby College)

  • Yaojue Xu

    (Colby College)

Abstract
In this paper, we construct a class of strictly consistent scoring functions based on the Bregman divergence measure, which jointly elicit the mean and variance. We use the scoring functions to develop a novel out-of-sample forecast encompassing test in volatility predictive models. We show the encompassing test is asymptotically normal. Simulation results demonstrate the merits of the proposed Bregman scoring functions and the forecast encompassing test. The forecast encompassing test exhibits a proper size and good power in finite samples. In an empirical application, we investigate the predictive ability of macroeconomic and financial variables in forecasting the equity premium volatility.

Suggested Citation

  • Tae-Hwy Lee & Ekaterina Seregina & Yaojue Xu, 2023. "Elicitability and Encompassing for Volatility Forecasts by Bregman Functions," Working Papers 202311, University of California at Riverside, Department of Economics.
    • Handle: RePEc:ucr:wpaper:202311
    as

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    File URL: https://economics.ucr.edu/repec/ucr/wpaper/202311.pdf
    File Function: First version, 2023
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    References listed on IDEAS

    as
    1. Ivo Welch & Amit Goyal, 2008. "A Comprehensive Look at The Empirical Performance of Equity Premium Prediction," The Review of Financial Studies, Society for Financial Studies, vol. 21(4), pages 1455-1508, July.
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    12. Patton, Andrew J., 2011. "Volatility forecast comparison using imperfect volatility proxies," Journal of Econometrics, Elsevier, vol. 160(1), pages 246-256, January.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    strictly consistent scoring function; elicitability; Bregman divergence; Granger-causality; encompassing; model averaging; equity premium.;
    All these keywords.

    JEL classification:

    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • E37 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Forecasting and Simulation: Models and Applications
    • E27 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - Forecasting and Simulation: Models and Applications

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