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A Spectral Measure for the Information Loss of Temporal Aggregation


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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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).

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