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Time series modeling of histogram-valued data: The daily histogram time series of S&P500 intradaily returns

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  • González-Rivera, Gloria
  • Arroyo, Javier

Abstract

Histogram time series (HTS) and interval time series (ITS) are examples of symbolic data sets. Though there have been methodological developments in a cross-sectional environment, they have been scarce in a time series setting. Arroyo, González-Rivera, and Maté (2011) analyze various forecasting methods for HTS and ITS, adapting smoothing filters and nonparametric algorithms such as the k-NN. Though these methods are very flexible, they may not be the true underlying data generating process (DGP). We present the first step in the search for a DGP by focusing on the autocorrelation functions (ACFs) of HTS and ITS. We analyze the ACF of the daily histogram of 5-minute intradaily returns to the S&P500 index in 2007 and 2008. There are clusters of high/low activity that generate a strong, positive, and persistent autocorrelation, pointing towards some autoregressive process for HTS. Though smoothing and k-NN may not be the true DGPs, we find that they are very good approximations because they are able to capture almost all of the original autocorrelation. However, there seems to be some structure left in the data that will require new modelling techniques. As a byproduct, we also analyze the [90,100%] quantile interval. By using all of the information contained in the histogram, we find that there are advantages in the estimation and prediction of a specific interval.

Suggested Citation

  • González-Rivera, Gloria & Arroyo, Javier, 2012. "Time series modeling of histogram-valued data: The daily histogram time series of S&P500 intradaily returns," International Journal of Forecasting, Elsevier, vol. 28(1), pages 20-33.
    • Handle: RePEc:eee:intfor:v:28:y:2012:i:1:p:20-33
    DOI: 10.1016/j.ijforecast.2011.02.007
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    References listed on IDEAS

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    1. 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.
    2. Arroyo, Javier & Maté, Carlos, 2009. "Forecasting histogram time series with k-nearest neighbours methods," International Journal of Forecasting, Elsevier, vol. 25(1), pages 192-207.
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    Citations

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    Cited by:

    1. Miguel de Carvalho & Gabriel Martos, 2022. "Modeling interval trendlines: Symbolic singular spectrum analysis for interval time series," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 41(1), pages 167-180, January.
    2. Sun, Yuying & Zhang, Xinyu & Wan, Alan T.K. & Wang, Shouyang, 2022. "Model averaging for interval-valued data," European Journal of Operational Research, Elsevier, vol. 301(2), pages 772-784.
    3. Dias, Sónia & Brito, Paula & Amaral, Paula, 2021. "Discriminant analysis of distributional data via fractional programming," European Journal of Operational Research, Elsevier, vol. 294(1), pages 206-218.
    4. Zheng, Lingwei & Su, Ran & Sun, Xinyu & Guo, Siqi, 2023. "Historical PV-output characteristic extraction based weather-type classification strategy and its forecasting method for the day-ahead prediction of PV output," Energy, Elsevier, vol. 271(C).
    5. Luis Lorenzo & Javier Arroyo, 2022. "Analysis of the cryptocurrency market using different prototype-based clustering techniques," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 8(1), pages 1-46, December.
    6. Buansing, T.S. Tuang & Golan, Amos & Ullah, Aman, 2020. "An information-theoretic approach for forecasting interval-valued SP500 daily returns," International Journal of Forecasting, Elsevier, vol. 36(3), pages 800-813.
    7. Antonio Balzanella & Antonio Irpino, 2020. "Spatial prediction and spatial dependence monitoring on georeferenced data streams," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 29(1), pages 101-128, March.
    8. Wilson Ye Chen & Gareth W. Peters & Richard H. Gerlach & Scott A. Sisson, 2017. "Dynamic Quantile Function Models," Papers 1707.02587, arXiv.org, revised May 2021.
    9. Paravee Maneejuk & Nootchanat Pirabun & Suphawit Singjai & Woraphon Yamaka, 2021. "Currency Hedging Strategies Using Histogram-Valued Data: Bivariate Markov Switching GARCH Models," Mathematics, MDPI, vol. 9(21), pages 1-20, November.

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