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Analysis of dependent data aggregated into intervals

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  • Samadi, S. Yaser
  • Billard, Lynne

Abstract

Many series of data record individual observations as intervals, such as stock market values with daily high-low values, or minimum and maximum monthly temperatures, recorded over time. With the advent of massively large data sets from contemporary computers, it is frequently the case that observations are aggregated into (meaningful) classes of observations, so that resulting data are perforce intervals (or histograms, or other forms of so-called symbolic data). What is known is that taking the average stock market price, or average temperature results in a loss of information. Therefore, this article looks at autocovariance/autocorrelation functions for interval-valued autoregressive series models. Maximum likelihood estimators are derived by exploiting the ideas of composite likelihood and the pairwise likelihood of Lindsay (1988) and Davis and Yau (2011). Different internal distributions of the intervals themselves are also studied. Asymptotic properties of these estimators are obtained. A simulation study shows that the new estimators perform considerably better than those obtained from the set-valued estimators of Wang et al. (2016).

Suggested Citation

  • Samadi, S. Yaser & Billard, Lynne, 2021. "Analysis of dependent data aggregated into intervals," Journal of Multivariate Analysis, Elsevier, vol. 186(C).
    • Handle: RePEc:eee:jmvana:v:186:y:2021:i:c:s0047259x21000956
    DOI: 10.1016/j.jmva.2021.104817
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    References listed on IDEAS

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    1. Wang, Xun & Zhang, Zhongzhan & Li, Shoumei, 2016. "Set-valued and interval-valued stationary time series," Journal of Multivariate Analysis, Elsevier, vol. 145(C), pages 208-223.
    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. X. Zhang & B. Beranger & S. A. Sisson, 2020. "Constructing likelihood functions for interval‐valued random variables," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 47(1), pages 1-35, March.
    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. Sun, Yuying & Han, Ai & Hong, Yongmiao & Wang, Shouyang, 2018. "Threshold autoregressive models for interval-valued time series data," Journal of Econometrics, Elsevier, vol. 206(2), pages 414-446.
    6. Joe, Harry & Lee, Youngjo, 2009. "On weighting of bivariate margins in pairwise likelihood," Journal of Multivariate Analysis, Elsevier, vol. 100(4), pages 670-685, April.
    7. Javier Arroyo & Rosa Espínola & Carlos Maté, 2011. "Different Approaches to Forecast Interval Time Series: A Comparison in Finance," Computational Economics, Springer;Society for Computational Economics, vol. 37(2), pages 169-191, February.
    8. Alexander Shapiro & Jos Berge, 2002. "Statistical inference of minimum rank factor analysis," Psychometrika, Springer;The Psychometric Society, vol. 67(1), pages 79-94, March.
    9. Maia, André Luis Santiago & de Carvalho, Francisco de A.T., 2011. "Holt's exponential smoothing and neural network models for forecasting interval-valued time series," International Journal of Forecasting, Elsevier, vol. 27(3), pages 740-759, July.
    10. 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.
    11. D. G. Malcolm & J. H. Roseboom & C. E. Clark & W. Fazar, 1959. "Application of a Technique for Research and Development Program Evaluation," Operations Research, INFORMS, vol. 7(5), pages 646-669, October.
    12. Gloria Gonzalez-Rivera & Javier Arroyo & Carlos Mate & A. Munoz San Roque, 2011. "Smoothing Methods for Histogram-valued Time Series. An Application to Value-at-Risk," Working Papers 201433, University of California at Riverside, Department of Economics.
    13. Varin, Cristiano & Vidoni, Paolo, 2006. "Pairwise likelihood inference for ordinal categorical time series," Computational Statistics & Data Analysis, Elsevier, vol. 51(4), pages 2365-2373, December.
    14. Maia, André Luis Santiago & de Carvalho, Francisco de A.T., 2011. "Holt’s exponential smoothing and neural network models for forecasting interval-valued time series," International Journal of Forecasting, Elsevier, vol. 27(3), pages 740-759.
    15. Ai Han & Yongmiao Hong & Shouyang Wang & Xin Yun, 2016. "A Vector Autoregressive Moving Average Model for Interval-Valued Time Series Data," Advances in Econometrics, in: Essays in Honor of Aman Ullah, volume 36, pages 417-460, Emerald Group Publishing Limited.
    16. Charles E. Clark, 1962. "Letter to the Editor---The PERT Model for the Distribution of an Activity Time," Operations Research, INFORMS, vol. 10(3), pages 405-406, June.
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    1. S. Yaser Samadi & L. Billard & Jiin-Huarng Guo & Wei Xu, 2024. "MLE for the parameters of bivariate interval-valued model," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 18(4), pages 827-850, December.

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