Density Forecast of Financial Returns Using Decomposition and Maximum Entropy

Tae Hwy Lee, Wang He (), Xi Zhou () and Zhang Ru ()
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Wang He: Department of Insurance, University of International Business and Economics, Beijing, China
Xi Zhou: Citigroup, Dallas, USA
Zhang Ru: JPMorgan Chase, Dallas, USA

Journal of Econometric Methods, 2023, vol. 12, issue 1, 57-83

Abstract: We consider a multiplicative decomposition of the financial returns to improve the density forecasts of financial returns. The multiplicative decomposition is based on the identity that financial return is the product of its absolute value and its sign. Advantages of modeling the two components are discussed. To reduce the effect of the estimation error due to the multiplicative decomposition in estimation of the density forecast model, we impose a moment constraint that the conditional mean forecast is set to match with the sample mean. Imposing such a moment constraint operates a shrinkage and tilts the density forecast of the decomposition model to produce the improved maximum entropy density forecast. An empirical application to forecasting density of the daily stock returns demonstrates the benefits of using the decomposition and imposing the moment constraint to obtain the improved density forecast. We evaluate the density forecast by comparing the logarithmic score (LS), the quantile score (QS), and the continuous ranked probability score (CRPS). We contribute to the literature on the density forecast and the decomposition models by showing that the density forecast of the decomposition model can be improved by imposing a sensible constraint in the maximum entropy framework.

Keywords: decomposition; copula; moment constraint; maximum entropy; density forecast; logarithmic score; quantile score; VaR; continuous ranked probability score (search for similar items in EconPapers)
JEL-codes: C1 C3 C5 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1515/jem-2020-0014

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