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Time Series Quantile Regression Using Random Forests

Author

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  • Hiroshi Shiraishi
  • Tomoshige Nakamura
  • Ryotato Shibuki

Abstract

We discuss an application of Generalized Random Forests (GRF) proposed to quantile regression for time series data. We extended the theoretical results of the GRF consistency for i.i.d. data to time series data. In particular, in the main theorem, based only on the general assumptions for time series data and trees, we show that the tsQRF (time series Quantile Regression Forest) estimator is consistent. Compare with existing article, different ideas are used throughout the theoretical proof. In addition, a simulation and real data analysis were conducted. In the simulation, the accuracy of the conditional quantile estimation was evaluated under time series models. In the real data using the Nikkei Stock Average, our estimator is demonstrated to capture volatility more efficiently, thus preventing underestimation of uncertainty.

Suggested Citation

  • Hiroshi Shiraishi & Tomoshige Nakamura & Ryotato Shibuki, 2024. "Time Series Quantile Regression Using Random Forests," Journal of Time Series Analysis, Wiley Blackwell, vol. 45(4), pages 639-659, July.
    • Handle: RePEc:bla:jtsera:v:45:y:2024:i:4:p:639-659
    DOI: 10.1111/jtsa.12731
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    References listed on IDEAS

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    1. Stefan Wager & Susan Athey, 2018. "Estimation and Inference of Heterogeneous Treatment Effects using Random Forests," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 113(523), pages 1228-1242, July.
    2. Cai, Zongwu & Wang, Xian, 2008. "Nonparametric estimation of conditional VaR and expected shortfall," Journal of Econometrics, Elsevier, vol. 147(1), pages 120-130, November.
    3. Hall, Peter & Wolff, Rodney C. L. & Yao, Qiwei, 1999. "Methods for estimating a conditional distribution function," LSE Research Online Documents on Economics 6631, London School of Economics and Political Science, LSE Library.
    4. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
    5. Robert F. Engle & Simone Manganelli, 2004. "CAViaR: Conditional Autoregressive Value at Risk by Regression Quantiles," Journal of Business & Economic Statistics, American Statistical Association, vol. 22, pages 367-381, October.
    6. Cai, Zongwu, 2002. "Regression Quantiles For Time Series," Econometric Theory, Cambridge University Press, vol. 18(1), pages 169-192, February.
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