Understanding temporal aggregation effects on kurtosis in financial indices

Offer Lieberman, Peter C.B. Phillips

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


Indices of financial returns typically display sample kurtosis that declines towards the Gaussian value 3 as the sampling interval increases. This paper uses stochastic unit root (STUR) and continuous time analysis to explain the phenomenon. Limit theory for the sample kurtosis reveals that STUR specifications provide two sources of excess kurtosis, both of which decline with the sampling interval. Limiting kurtosis is shown to be random and is a functional of the limiting price process. Using a continuous time version of the model under no-drift, local drift, and drift inclusions, we suggest a new continuous time kurtosis measure for financial returns that assists in reconciling these models with the empirical kurtosis characteristics of returns. Simulations are reported and applications to several financial indices demonstrate the usefulness of this approach.

Original languageEnglish
Pages (from-to)25-46
Number of pages22
JournalJournal of Econometrics
Issue number1
StatePublished - Mar 2022

Bibliographical note

Funding Information:
Support from Israel Science Foundation grant No. 1182-17 is gratefully acknowledged.Research support is acknowledged from the Kelly Fund at the University of Auckland and the National Science Foundation under Grant No. SES 18-50860.

Publisher Copyright:
© 2020 Elsevier B.V.


  • Autoregression
  • Diffusion
  • Kurtosis
  • Stochastic unit root
  • Time-varying coefficients


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