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A Spectral Measure for the Information Loss of Temporal Aggregation

Journal of Statistical Theory and Practice volume 14, Article number: 34 (2020) Cite this article

Abstract

We develop a spectral measure to trace the relative distance and direction of information loss resulting from temporal aggregation of a stationary time series process. Temporal aggregation is utilized as not only the reduction in the data size but also the summarization of process information. However, it is inevitable that the aggregation leads to substantial structural changes, the so-called information loss on the original process structure. Using the proposed measure, we quantify the aggregation effect in terms of the relative distance of the standardized spectral densities between “the original process to white noise” and “the aggregate process to white noise.” In addition, we suggest a guideline to identify the marginal order of temporal aggregation where the aggregation produces less information loss while providing more effective data reduction. As an illustration, we analyze the monthly CRSP log returns between January 1926 and December 2008.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Loyola University Maryland, 4501 N. Charles Street, Baltimore, MD, 21210, USA

    Bu Hyoung Lee

  2. Department of Statistics, Seoul National University, 1 Gwanak-ro, Gwanak-gu, Seoul, 08826, South Korea

    Junyong Park

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  1. Bu Hyoung Lee
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  2. Junyong Park
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Correspondence to Bu Hyoung Lee.

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Lee, B.H., Park, J. A Spectral Measure for the Information Loss of Temporal Aggregation. J Stat Theory Pract 14, 34 (2020). https://doi.org/10.1007/s42519-020-00099-3

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  • DOI: https://doi.org/10.1007/s42519-020-00099-3

Keywords

  • Temporal aggregation
  • Information loss
  • Spectral measure
  • Marginal aggregation
  • CRSP log returns