Research Papers

A New Approach for Forecasting the Price Range With Financial Interval-Valued Time Series Data

[+] Author and Article Information
Wei Yang

School of Mathematical Science, Institute of Management and Decision, Shanxi University, Taiyuan, Shanxi 030006, Chinae-mail: yangwei@sxu.edu.cn

Ai Han

Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, Chinae-mail: hanai@amss.ac.cn

1Corresponding author.

Manuscript received August 30, 2014; final manuscript received January 15, 2015; published online April 20, 2015. Assoc. Editor: Athanasios Pantelous.

ASME J. Risk Uncertainty Part B 1(2), 021004 (Apr 20, 2015) (8 pages) Paper No: RISK-14-1044; doi: 10.1115/1.4029751 History: Received August 30, 2014; Accepted February 05, 2015; Online April 20, 2015

This paper proposes an interval-based methodology to model and forecast the price range or range-based volatility process of financial asset prices. Comparing with the existing volatility models, the proposed model utilizes more information contained in the interval time series than using the range information only or modeling the high and low price processes separately. An empirical study of the U.S. stock market daily data shows that the proposed interval-based model produces more accurate range forecasts than the classic point-based linear models for range process, in terms of both in-sample and out-of-sample forecasts. The statistical tests show that the forecasting advantages of the interval-based model are statistically significant in most cases. In addition, some stability tests have been conducted for ascertaining the advantages of the interval-based model through different sample windows and forecasting periods, which reveals similar results. This study provides a new interval-based perspective for volatility modeling and forecasting of financial time series data.

Copyright © 2015 by ASME
Your Session has timed out. Please sign back in to continue.


Merton, R. C., 1969, “Lifetime Portfolio Selection Under Uncertainty: The Continuous-Time Case,” Rev. Econ. Stat., 51(3), pp. 247–257. 10.2307/1926560
Black, F., and Scholes, M., 1973, “The Pricing of Options and Corporate Liabilities,” J. Polit. Econ., 81(3), pp. 637–654. 10.1086/jpe.1973.81.issue-3
Engle, R. F., 1982, “Autoregressive Conditional Heteroscedasticity With Estimates of the Variance of United Kingdom Inflation,” Econometrica, 50(4), pp. 987–1008. 10.2307/1912773
Bollerslev, T., 1986, “Generalized Autoregressive Conditional Heteroskedasticity,” J. Econometrics, 31(3), pp. 307–327. 10.1016/0304-4076(86)90063-1
Hull, J., and White, A., 1987, “The Pricing of Options on Assets with Stochastic Volatilities,” J. Financ., 42(2), pp. 281–300. 10.1111/j.1540-6261.1987.tb02568.x
Poon, S. H., and Granger, C. W. J., 2003, “Forecasting the Volatility in Financial Market: A Review,” J. Econ. Lit., 41(2), pp. 478–539. 10.1257/jel.41.2.478
Francq, C., and Zakoian, J. M., 2010, GARCH Models: Structure, Statistical Inference and Financial Applications, Wiley, Hoboken, NJ.
Alizadeh, S., Brandt, M. W., and Diebold, F. X., 2002, “Range-Based Estimation of Stochastic Volatility Models,” J. Financ., 57(3), pp. 1047–1092. 10.1111/1540-6261.00454
Brandt, M. W., and Diebold, F. X., 2006, “A No-Arbitrage Approach to Range-Based Estimation of Return Covariances and Correlations,” J. Bus., 79(1), pp. 61–74. 10.3386/w9664
Parkinson, M., 1980, “The Extreme Value Method for Estimating the Variance of the Rate of Return,” J. Bus., 53(1), pp. 61–65. 10.1086/296071
Kunitomo, N., 1992, “Improving the Parkinson Method of Estimating Security Price Volatilities,” J. Bus., 65(2), pp. 295–302. 10.1086/296570
Yang, D., and Zhang, Q., 2000, “Drift-Independent Volatility Estimation Based on High, Low, Open and Close Prices,” J. Bus., 73(3), pp. 477–491. 10.1086/209650
Chou, R. Y., 2005, “Forecasting Financial Volatilities with Extreme Values: The Conditional Autoregressive Range (CARR) Model,” J. Money Credit Bank., 37(3), pp. 561–582. [CrossRef]
Fernandes, M., de Sá Mota, B., and Rocha, G., 2005, “A Multivariate Conditional Autoregressive Range Model,” Econ. Lett., 86(3), pp. 435–440. 10.1016/j.econlet.2004.09.005
Martens, M., and van Dijk, D., 2007, “Measuring Volatility with the Realized Range,” J. Econometrics, 138(1), pp. 181–207. 10.1016/j.jeconom.2006.05.019
Christensen, K., and Podolskij, M., 2007, “Realized Range-Based Estimation of Integrated Variance,” J. Econometrics, 141(2), pp. 323–349. [CrossRef]
Brownlees, C. T., and Gallo, G. M., 2010, “Comparison of Volatility Measures: A Risk Management Perspective,” J. Financ. Econometrics, 8(1), pp. 29–56. 10.1093/jjfinec/nbp009
Cheung, Y. W., 2007, “An Empirical Model of Daily Highs and Lows,” Int. J. Financ. Econ., 12(1), pp. 1–20. 10.1002/ijfe.303
Cheung, Y. L., Cheung, Y. W., and Wan, A. T., 2009, “A High-Low Model of Daily Stock Price Ranges,” J. Forecast., 28(2), pp. 103–119. 10.1002/for.1087
Bertrand, P., and Goupil, F., 2000, “Descriptive Statistic for Symbolic Data,” Analysis of Symbolic Data, H.-H. Bock, and E. Diday, eds., Springer, Heidelberg, Germany, pp. 106–124.
Billard, L., and Diday, E., 2000, “Regression Analysis for Interval-Valued Data,” Data Analysis, Classification and Related Methods, Proceedings of the 7th Conference of the International Federation of Classification Societies (IFCS00), Springer, Namur, Belgium, pp. 369–374.
Billard, L., and Diday, E., 2002, “Symbolic Regression Analysis,” Classification, Clustering and Data Analysis, Proceedings of the 8th Conference of the International Federation of Classification Societies (IFCS02), Springer, Cracow, Poland, pp. 281–288.
Billard, L., and Diday, E., 2003, “From the Statistics of Data to the Statistics of Knowledge: Symbolic Data Analysis,” J. Am. Stat. Assoc., 98(462), pp. 470–487. 10.1198/016214503000242
Lima Neto, E. A., de Carvalho, F. A. T., and Freire, E. S., 2008, “Centre and Range Method for Fitting a Linear Regression Model to Symbolic Interval Data,” Comput. Stat. Data Anal., 52(3), pp. 1500–1515. 10.1016/j.csda.2007.04.014
Lima Neto, E. A., and de Carvalho, F. A. T., 2010, “Constrained Linear Regression Models for Symbolic Interval-Valued Variables,” Comput. Stat. Data Anal., 54(2), pp. 333–347. 10.1016/j.csda.2009.08.010
Han, A., Hong, Y. M., and Wang, S. Y., 2012, “Autoregressive Conditional Models for Interval-Valued Time Series Data.” Available at: http://economics.yale.edu/sites/default/files/hong-120926.pdf.
Yang, W., Han, A., Cai, K., and Wang, S. Y., 2012, “ACIX Model With Interval Dummy Variables and its Application in Forecasting Interval-Valued Crude Oil Prices,” Procedia Comput. Sci., 9(2), pp. 1273–1282. 10.1016/j.procs.2012.04.139
Yang, W., Han, A., and Wang, S. Y., 2013, “Analysis of the Interaction Between Crude Oil Price and US Stock Market Based on Interval Data,” Int. J. Energy Stat., 1(2), pp. 85–98. 10.1142/S2335680413500063
Diebold, F. X., and Mariano, R. S., 1995, “Comparing Predictive Accuracy,” J. Bus. Econ. Stat., 13(3), pp. 253–263. 10.1080/07350015.1995.10524599
Harvey, D., Leybourne, S., and Newbold, P., 1997, “Testing the Equality of Prediction Mean Squared Errors,” Int. J. Forecast., 13(2), pp. 281–291. 10.1016/S0169-2070(96)00719-4


Grahic Jump Location
Fig. 1

Daily lows, highs, and ranges of the interval-valued S&P500 price index




Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Articles from Part A: Civil Engineering
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In