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Symbolic interval-valued data analysis for time series based on auto-interval-regressive models

Author

Listed:
  • Liang-Ching Lin

    (National Cheng Kung University)

  • Hsiang-Lin Chien

    (National Cheng Kung University)

  • Sangyeol Lee

    (Seoul National University)

Abstract

This study considers interval-valued time series data. To characterize such data, we propose an auto-interval-regressive (AIR) model using the order statistics from normal distributions. Furthermore, to better capture the heteroscedasticity in volatility, we design a heteroscedastic volatility AIR (HVAIR) model. We derive the likelihood functions of the AIR and HVAIR models to obtain the maximum likelihood estimator. Monte Carlo simulations are then conducted to evaluate our methods of estimation and confirm their validity. A real data example from the S&P 500 Index is used to demonstrate our method.

Suggested Citation

  • Liang-Ching Lin & Hsiang-Lin Chien & Sangyeol Lee, 2021. "Symbolic interval-valued data analysis for time series based on auto-interval-regressive models," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 30(1), pages 295-315, March.
    • Handle: RePEc:spr:stmapp:v:30:y:2021:i:1:d:10.1007_s10260-020-00525-7
    DOI: 10.1007/s10260-020-00525-7
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    References listed on IDEAS

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    1. Lin, Wei & González-Rivera, Gloria, 2016. "Interval-valued time series models: Estimation based on order statistics exploring the Agriculture Marketing Service data," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 694-711.
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    3. Gloria González-Rivera & Wei Lin, 2013. "Constrained Regression for Interval-Valued Data," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 31(4), pages 473-490, October.
    4. Paulo Teles & Paula Brito, 2015. "Modeling Interval Time Series with Space–Time Processes," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 44(17), pages 3599-3627, September.
    5. Paula Brito & A. Pedro Duarte Silva, 2012. "Modelling interval data with Normal and Skew-Normal distributions," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(1), pages 3-20, March.
    6. Lima Neto, Eufrasio de A. & de Carvalho, Francisco de A.T., 2008. "Centre and Range method for fitting a linear regression model to symbolic interval data," Computational Statistics & Data Analysis, Elsevier, vol. 52(3), pages 1500-1515, January.
    7. 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.
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    Cited by:

    1. Kejia Yan & Rakesh Gupta & Sama Haddad, 2022. "Statistical Analysis Dow Jones Stock Index—Cumulative Return Gap and Finite Difference Method," JRFM, MDPI, vol. 15(2), pages 1-44, February.

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