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An Empirical Model of Daily Highs and Lows

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  • Yin-Wong Cheung

Abstract

We construct an empirical model for daily highs and daily lows of US stock indexes based on the intuition that highs and lows do not drift apart over time. Our empirical results show that daily highs and lows of three main US stock price indexes are cointegrated. Data on openings, closings, and trading volume are found to offer incremental explanatory power for variations in highs and lows within the VECM framework. With all these variables, the augmented VECM models explain 40% to 50% of variations in daily highs and lows. The generalized impulse response analysis shows that the responses of daily highs and daily lows to the shocks depend on whether data on openings, closings, and trading volume are included in the analysis.

Suggested Citation

  • Yin-Wong Cheung, 2006. "An Empirical Model of Daily Highs and Lows," CESifo Working Paper Series 1695, CESifo.
    • Handle: RePEc:ces:ceswps:_1695
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    Cited by:

    1. Andrey Kudryavtsev, 2012. "Short-Term Stock Price Reversals May Be Reversed," International Journal of Business and Economic Sciences Applied Research (IJBESAR), Democritus University of Thrace (DUTH), Kavala Campus, Greece, vol. 5(3), pages 129-146, December.
    2. Huang, Wenyang & Wang, Huiwen & Qin, Haotong & Wei, Yigang & Chevallier, Julien, 2022. "Convolutional neural network forecasting of European Union allowances futures using a novel unconstrained transformation method," Energy Economics, Elsevier, vol. 110(C).
    3. Leandro Maciel, 2020. "Technical analysis based on high and low stock prices forecasts: evidence for Brazil using a fractionally cointegrated VAR model," Empirical Economics, Springer, vol. 58(4), pages 1513-1540, April.
    4. Huang, Wenyang & Wang, Huiwen & Wei, Yigang, 2023. "Identifying the determinants of European carbon allowances prices: A novel robust partial least squares method for open-high-low-close data," International Review of Financial Analysis, Elsevier, vol. 90(C).
    5. Angela He & Alan Wan, 2009. "Predicting daily highs and lows of exchange rates: a cointegration analysis," Journal of Applied Statistics, Taylor & Francis Journals, vol. 36(11), pages 1191-1204.
    6. Baruník, Jozef & Dvořáková, Sylvie, 2015. "An empirical model of fractionally cointegrated daily high and low stock market prices," Economic Modelling, Elsevier, vol. 45(C), pages 193-206.
    7. Xiong, Tao & Li, Chongguang & Bao, Yukun, 2017. "Interval-valued time series forecasting using a novel hybrid HoltI and MSVR model," Economic Modelling, Elsevier, vol. 60(C), pages 11-23.
    8. Caporin, Massimiliano & Ranaldo, Angelo & Santucci de Magistris, Paolo, 2013. "On the predictability of stock prices: A case for high and low prices," Journal of Banking & Finance, Elsevier, vol. 37(12), pages 5132-5146.
    9. González-Rivera, Gloria & Rodríguez Caballero, Carlos Vladimir, 2023. "Modelling intervals of minimum/maximum temperatures in the Iberian Peninsula," DES - Working Papers. Statistics and Econometrics. WS 37968, Universidad Carlos III de Madrid. Departamento de Estadística.
    10. OlaOluwa S. Yaya & Xuan Vinh Vo & Ahamuefula E. Ogbonna & Adeolu O. Adewuyi, 2022. "Modelling cryptocurrency high–low prices using fractional cointegrating VAR," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 27(1), pages 489-505, January.
    11. Yan-Leung Cheung & Yin-Wong Cheung & Alan T. K. Wan, 2009. "A high-low model of daily stock price ranges," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 28(2), pages 103-119.
    12. Paulo Rodrigues & Nazarii Salish, 2015. "Modeling and forecasting interval time series with threshold models," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 9(1), pages 41-57, March.
    13. Alia Afzal & Philipp Sibbertsen, 2021. "Modeling fractional cointegration between high and low stock prices in Asian countries," Empirical Economics, Springer, vol. 60(2), pages 661-682, February.
    14. Hu, Zhongyi & Bao, Yukun & Chiong, Raymond & Xiong, Tao, 2015. "Mid-term interval load forecasting using multi-output support vector regression with a memetic algorithm for feature selection," Energy, Elsevier, vol. 84(C), pages 419-431.
    15. Awartani, Basel & Maghyereh, Aktham Issa, 2013. "Dynamic spillovers between oil and stock markets in the Gulf Cooperation Council Countries," Energy Economics, Elsevier, vol. 36(C), pages 28-42.
    16. Zhu, Mengrui & Xu, Hua & Wang, Minggang & Tian, Lixin, 2024. "Carbon price interval prediction method based on probability density recurrence network and interval multi-layer perceptron," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 636(C).
    17. Javier Arroyo & Rosa Espínola & Carlos Maté, 2011. "Different Approaches to Forecast Interval Time Series: A Comparison in Finance," Computational Economics, Springer;Society for Computational Economics, vol. 37(2), pages 169-191, February.
    18. Caporale, Guglielmo Maria & Gil-Alana, Luis A. & Poza, Carlos, 2020. "High and low prices and the range in the European stock markets: A long-memory approach," Research in International Business and Finance, Elsevier, vol. 52(C).
    19. Yaya, OlaOluwa S & Gil-Alana, Luis A., 2018. "High and Low Intraday Commodity Prices: A Fractional Integration and Cointegration Approach," MPRA Paper 90518, University Library of Munich, Germany.
    20. Ni, Yensen & Liao, Yi-Ching & Huang, Paoyu, 2015. "MA trading rules, herding behaviors, and stock market overreaction," International Review of Economics & Finance, Elsevier, vol. 39(C), pages 253-265.
    21. Wenyang Huang & Huiwen Wang & Shanshan Wang, 2021. "Dimension reduction of open-high-low-close data in candlestick chart based on pseudo-PCA," Papers 2103.16908, arXiv.org.
    22. García-Ascanio, Carolina & Maté, Carlos, 2010. "Electric power demand forecasting using interval time series: A comparison between VAR and iMLP," Energy Policy, Elsevier, vol. 38(2), pages 715-725, February.
    23. Paulo M.M. Rodrigues & Nazarii Salish, 2011. "Modeling and Forecasting Interval Time Series with Threshold Models: An Application to S&P500 Index Returns," Working Papers w201128, Banco de Portugal, Economics and Research Department.
    24. Huiwen Wang & Wenyang Huang & Shanshan Wang, 2021. "Forecasting open-high-low-close data contained in candlestick chart," Papers 2104.00581, arXiv.org.
    25. Cheung, Yan-Leung & Cheung, Yin-Wong & He, Angela W.W. & Wan, Alan T.K., 2010. "A trading strategy based on Callable Bull/Bear Contracts," Pacific-Basin Finance Journal, Elsevier, vol. 18(2), pages 186-198, April.

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    More about this item

    Keywords

    high; low open; close; trading volume; VECM model;
    All these keywords.

    JEL classification:

    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)

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