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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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