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Hedging Forecast Combinations With an Application to the Random Forest

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  • Elliot Beck
  • Damian Kozbur
  • Michael Wolf

Abstract

This papers proposes a generic, high-level methodology for generating forecast combinations that would deliver the optimal linearly combined forecast in terms of the mean-squared forecast error if one had access to two population quantities: the mean vector and the covariance matrix of the vector of individual forecast errors. We point out that this problem is identical to a mean-variance portfolio construction problem, in which portfolio weights correspond to forecast combination weights. We allow negative forecast weights and interpret such weights as hedging over and under estimation risks across estimators. This interpretation follows directly as an implication of the portfolio analogy. We demonstrate our method's improved out-of-sample performance relative to standard methods in combining tree forecasts to form weighted random forests in 14 data sets.

Suggested Citation

  • Elliot Beck & Damian Kozbur & Michael Wolf, 2023. "Hedging Forecast Combinations With an Application to the Random Forest," Papers 2308.15384, arXiv.org, revised Aug 2023.
  • Handle: RePEc:arx:papers:2308.15384
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    References listed on IDEAS

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    1. Olivier Ledoit & Michael Wolf, 2022. "The Power of (Non-)Linear Shrinking: A Review and Guide to Covariance Matrix Estimation [Design-Free Estimation of Variance Matrices]," Journal of Financial Econometrics, Oxford University Press, vol. 20(1), pages 187-218.
    2. Bergmeir, Christoph & Hyndman, Rob J. & Koo, Bonsoo, 2018. "A note on the validity of cross-validation for evaluating autoregressive time series prediction," Computational Statistics & Data Analysis, Elsevier, vol. 120(C), pages 70-83.
    3. Ravi Jagannathan & Tongshu Ma, 2003. "Risk Reduction in Large Portfolios: Why Imposing the Wrong Constraints Helps," Journal of Finance, American Finance Association, vol. 58(4), pages 1651-1683, August.
    4. Graham Elliott & Allan Timmermann, 2016. "Economic Forecasting," Economics Books, Princeton University Press, edition 1, number 10740.
    5. Victor DeMiguel & Lorenzo Garlappi & Francisco J. Nogales & Raman Uppal, 2009. "A Generalized Approach to Portfolio Optimization: Improving Performance by Constraining Portfolio Norms," Management Science, INFORMS, vol. 55(5), pages 798-812, May.
    6. Graham Elliott & Allan Timmermann, 2016. "Forecasting in Economics and Finance," Annual Review of Economics, Annual Reviews, vol. 8(1), pages 81-110, October.
    7. Sancetta, Alessio, 2008. "Sample covariance shrinkage for high dimensional dependent data," Journal of Multivariate Analysis, Elsevier, vol. 99(5), pages 949-967, May.
    8. Robert F. Engle & Olivier Ledoit & Michael Wolf, 2019. "Large Dynamic Covariance Matrices," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 37(2), pages 363-375, April.
    9. repec:bla:jfinan:v:58:y:2003:i:4:p:1651-1684 is not listed on IDEAS
    10. Wright, Marvin N. & Ziegler, Andreas, 2017. "ranger: A Fast Implementation of Random Forests for High Dimensional Data in C++ and R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 77(i01).
    11. Bodnar, Taras & Okhrin, Ostap & Parolya, Nestor, 2019. "Optimal shrinkage estimator for high-dimensional mean vector," Journal of Multivariate Analysis, Elsevier, vol. 170(C), pages 63-79.
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