IDEAS home Printed from
   My bibliography  Save this paper

A High-Low Model of Daily Stock Price Ranges


  • Yan-Leung Cheung

    (City University of Hong Kong)

  • Yin-Wong Cheung

    (University of California, Santa Cruz)

  • Alan T. K. Wan

    (City University of Hong Kong)


We observe that daily highs and lows of stock prices do not diverge over time and, hence, adopt the cointegration concept and the related vector error correction model (VECM) to model the daily high, the daily low, and the associated daily range data. The in-sample results attest the importance of incorporating high-low interactions in modeling the range variable. In evaluating the out-of-sample forecast performance using both mean-squared forecast error and direction of change criteria, it is found that the VECM-based low and high forecasts offer some advantages over some alternative forecasts. The VECM-based range forecasts, on the other hand, do not always dominate - the forecast rankings depend on the choice of evaluation criterion and the variables being forecasted.

Suggested Citation

  • Yan-Leung Cheung & Yin-Wong Cheung & Alan T. K. Wan, 2009. "A High-Low Model of Daily Stock Price Ranges," Working Papers 032009, Hong Kong Institute for Monetary Research.
  • Handle: RePEc:hkm:wpaper:032009

    Download full text from publisher

    File URL:
    Download Restriction: no

    Other versions of this item:

    References listed on IDEAS

    1. Garman, Mark B & Klass, Michael J, 1980. "On the Estimation of Security Price Volatilities from Historical Data," The Journal of Business, University of Chicago Press, vol. 53(1), pages 67-78, January.
    2. A. Ronald Gallant & Chien-Te Hsu & George Tauchen, 1999. "Using Daily Range Data To Calibrate Volatility Diffusions And Extract The Forward Integrated Variance," The Review of Economics and Statistics, MIT Press, vol. 81(4), pages 617-631, November.
    3. Andersen, Torben G. & Bollerslev, Tim & Christoffersen, Peter F. & Diebold, Francis X., 2005. "Volatility forecasting," CFS Working Paper Series 2005/08, Center for Financial Studies (CFS).
    4. Johansen, Soren & Juselius, Katarina, 1990. "Maximum Likelihood Estimation and Inference on Cointegration--With Applications to the Demand for Money," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 52(2), pages 169-210, May.
    5. Diebold, Francis X & Mariano, Roberto S, 2002. "Comparing Predictive Accuracy," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 134-144, January.
    6. Christoffersen, Peter F & Diebold, Francis X, 1998. "Cointegration and Long-Horizon Forecasting," Journal of Business & Economic Statistics, American Statistical Association, vol. 16(4), pages 450-458, October.
    7. Engle, Robert F. & Gallo, Giampiero M., 2006. "A multiple indicators model for volatility using intra-daily data," Journal of Econometrics, Elsevier, vol. 131(1-2), pages 3-27.
    8. Yin-Wong Cheung, 2007. "An empirical model of daily highs and lows," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 12(1), pages 1-20.
    9. Michael P. Clements & David F.Hendry, 2001. "Forecasting with difference-stationary and trend-stationary models," Econometrics Journal, Royal Economic Society, vol. 4(1), pages 1-19.
    10. Cheung, Yin-Wong & Lai, Kon S, 1995. "Lag Order and Critical Values of the Augmented Dickey-Fuller Test," Journal of Business & Economic Statistics, American Statistical Association, vol. 13(3), pages 277-280, July.
    11. Abhyankar, Abhay & Sarno, Lucio & Valente, Giorgio, 2005. "Exchange rates and fundamentals: evidence on the economic value of predictability," Journal of International Economics, Elsevier, vol. 66(2), pages 325-348, July.
    12. Michael W. Brandt & Francis X. Diebold, 2006. "A No-Arbitrage Approach to Range-Based Estimation of Return Covariances and Correlations," The Journal of Business, University of Chicago Press, vol. 79(1), pages 61-74, January.
    13. Beckers, Stan, 1983. "Variances of Security Price Returns Based on High, Low, and Closing Prices," The Journal of Business, University of Chicago Press, vol. 56(1), pages 97-112, January.
    14. Fernandes, Marcelo & de Sa Mota, Bernardo & Rocha, Guilherme, 2005. "A multivariate conditional autoregressive range model," Economics Letters, Elsevier, vol. 86(3), pages 435-440, March.
    15. Parkinson, Michael, 1980. "The Extreme Value Method for Estimating the Variance of the Rate of Return," The Journal of Business, University of Chicago Press, vol. 53(1), pages 61-65, January.
    16. Parkinson, Michael, 1977. "Option Pricing: The American Put," The Journal of Business, University of Chicago Press, vol. 50(1), pages 21-36, January.
    17. Ser-Huang Poon & Clive W.J. Granger, 2003. "Forecasting Volatility in Financial Markets: A Review," Journal of Economic Literature, American Economic Association, vol. 41(2), pages 478-539, June.
    18. Yang, Dennis & Zhang, Qiang, 2000. "Drift-Independent Volatility Estimation Based on High, Low, Open, and Close Prices," The Journal of Business, University of Chicago Press, vol. 73(3), pages 477-491, July.
    19. Sassan Alizadeh & Michael W. Brandt & Francis X. Diebold, 2002. "Range-Based Estimation of Stochastic Volatility Models," Journal of Finance, American Finance Association, vol. 57(3), pages 1047-1091, June.
    20. Kunitomo, Naoto, 1992. "Improving the Parkinson Method of Estimating Security Price Volatilities," The Journal of Business, University of Chicago Press, vol. 65(2), pages 295-302, April.
    21. Cheung, Yin-Wong & Chinn, Menzie David, 2001. "Currency traders and exchange rate dynamics: a survey of the US market," Journal of International Money and Finance, Elsevier, vol. 20(4), pages 439-471, August.
    22. Harvey, David & Leybourne, Stephen & Newbold, Paul, 1997. "Testing the equality of prediction mean squared errors," International Journal of Forecasting, Elsevier, vol. 13(2), pages 281-291, June.
    23. Taylor, Mark P. & Allen, Helen, 1992. "The use of technical analysis in the foreign exchange market," Journal of International Money and Finance, Elsevier, vol. 11(3), pages 304-314, June.
    24. Johansen, Soren, 1991. "Estimation and Hypothesis Testing of Cointegration Vectors in Gaussian Vector Autoregressive Models," Econometrica, Econometric Society, vol. 59(6), pages 1551-1580, November.
    25. Chou, Ray Yeutien, 2005. "Forecasting Financial Volatilities with Extreme Values: The Conditional Autoregressive Range (CARR) Model," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 37(3), pages 561-582, June.
    26. Leitch, Gordon & Tanner, J Ernest, 1991. "Economic Forecast Evaluation: Profits versus the Conventional Error Measures," American Economic Review, American Economic Association, vol. 81(3), pages 580-590, June.
    27. Chinn, Menzie D. & Meese, Richard A., 1995. "Banking on currency forecasts: How predictable is change in money?," Journal of International Economics, Elsevier, vol. 38(1-2), pages 161-178, February.
    28. Cheung, Yin-Wong & Wong, Clement Yuk-Pang, 2000. "A survey of market practitioners' views on exchange rate dynamics," Journal of International Economics, Elsevier, vol. 51(2), pages 401-419, August.
    29. Mark, Nelson C, 1995. "Exchange Rates and Fundamentals: Evidence on Long-Horizon Predictability," American Economic Review, American Economic Association, vol. 85(1), pages 201-218, March.
    Full references (including those not matched with items on IDEAS)


    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.

    Cited by:

    1. He, Angela W.W. & Kwok, Jerry T.K. & Wan, Alan T.K., 2010. "An empirical model of daily highs and lows of West Texas Intermediate crude oil prices," Energy Economics, Elsevier, vol. 32(6), pages 1499-1506, November.
    2. 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.
    3. Henning Fischer & Ángela Blanco‐FERNÁndez & Peter Winker, 2016. "Predicting Stock Return Volatility: Can We Benefit from Regression Models for Return Intervals?," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 35(2), pages 113-146, March.
    4. 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.
    5. Tao Xiong & Yukun Bao & Zhongyi Hu, 2014. "Multiple-output support vector regression with a firefly algorithm for interval-valued stock price index forecasting," Papers 1401.1916,
    6. Gloria Gonzalez-Rivera & Javier Arroyo & Carlos Mate, 2011. "Forecasting with Interval and Histogram Data. Some Financial Applications," Working Papers 201438, University of California at Riverside, Department of Economics.
    7. Liu, Zhichao & Ma, Feng & Long, Yujia, 2015. "High and low or close to close prices? Evidence from the multifractal volatility," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 427(C), pages 50-61.
    8. Ai Han & Yanan He & Yongmiao Hong & Shouyang Wang, 2013. "Forecasting Interval-valued Crude Oil Prices via Autoregressive Conditional Interval Models," WISE Working Papers 2013-10-14, Wang Yanan Institute for Studies in Economics (WISE), Xiamen University.

    More about this item


    Daily High; Daily Low; VECM Model; Forecast Performance; Implied Volatility;

    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
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)

    NEP fields

    This paper has been announced in the following NEP Reports:


    Access and download statistics


    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:hkm:wpaper:032009. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (HKIMR). General contact details of provider: .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.