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Modeling financial interval time series

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  • Liang-Ching Lin
  • Li-Hsien Sun

Abstract

In financial economics, a large number of models are developed based on the daily closing price. When using only the daily closing price to model the time series, we may discard valuable intra-daily information, such as maximum and minimum prices. In this study, we propose an interval time series model, including the daily maximum, minimum, and closing prices, and then apply the proposed model to forecast the entire interval. The likelihood function and the corresponding maximum likelihood estimates (MLEs) are obtained by stochastic differential equation and the Girsanov theorem. To capture the heteroscedasticity of volatility, we consider a stochastic volatility model. The efficiency of the proposed estimators is illustrated by a simulation study. Finally, based on real data for S&P 500 index, the proposed method outperforms several alternatives in terms of the accurate forecast.

Suggested Citation

  • Liang-Ching Lin & Li-Hsien Sun, 2019. "Modeling financial interval time series," PLOS ONE, Public Library of Science, vol. 14(2), pages 1-20, February.
    • Handle: RePEc:plo:pone00:0211709
    DOI: 10.1371/journal.pone.0211709
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    References listed on IDEAS

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    1. Stein, Elias M & Stein, Jeremy C, 1991. "Stock Price Distributions with Stochastic Volatility: An Analytic Approach," The Review of Financial Studies, Society for Financial Studies, vol. 4(4), pages 727-752.
    2. Billard L. & Diday E., 2003. "From the Statistics of Data to the Statistics of Knowledge: Symbolic Data Analysis," Journal of the American Statistical Association, American Statistical Association, vol. 98, pages 470-487, January.
    3. Choi, ByoungSeon & Roh, JeongHo, 2013. "On the trivariate joint distribution of Brownian motion and its maximum and minimum," Statistics & Probability Letters, Elsevier, vol. 83(4), pages 1046-1053.
    4. Yacine Aït-Sahalia, 2005. "How Often to Sample a Continuous-Time Process in the Presence of Market Microstructure Noise," The Review of Financial Studies, Society for Financial Studies, vol. 18(2), pages 351-416.
    5. Gloria González-Rivera & Tae-Hwy Lee & Santosh Mishra, 2008. "Jumps in cross-sectional rank and expected returns: a mixture model," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 23(5), pages 585-606.
    6. Chen, Cathy W.S. & Gerlach, Richard & Lin, Edward M.H., 2008. "Volatility forecasting using threshold heteroskedastic models of the intra-day range," Computational Statistics & Data Analysis, Elsevier, vol. 52(6), pages 2990-3010, February.
    7. Andersen, Torben G. & Bollerslev, Tim & Diebold, Francis X. & Ebens, Heiko, 2001. "The distribution of realized stock return volatility," Journal of Financial Economics, Elsevier, vol. 61(1), pages 43-76, July.
    8. 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.
    9. 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.
    10. Akahori, Jiro & Song, Xiaoming & Wang, Tai-Ho, 2019. "Bridge representation and modal-path approximation," Stochastic Processes and their Applications, Elsevier, vol. 129(1), pages 174-204.
    11. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    12. Hull, John C & White, Alan D, 1987. "The Pricing of Options on Assets with Stochastic Volatilities," Journal of Finance, American Finance Association, vol. 42(2), pages 281-300, June.
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    Cited by:

    1. Zhu, Bangzhu & Wan, Chunzhuo & Wang, Ping, 2022. "Interval forecasting of carbon price: A novel multiscale ensemble forecasting approach," Energy Economics, Elsevier, vol. 115(C).

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