Understanding Temporal Aggregation Effects on Kurtosis in Financial Indices

40 Pages Posted: 11 Dec 2018

See all articles by Offer Lieberman

Offer Lieberman

Technion-Israel Institute of Technology - The William Davidson Faculty of Industrial Engineering & Management

Peter C. B. Phillips

University of Auckland Business School; Yale University - Cowles Foundation; Singapore Management University - School of Economics

Date Written: June 17, 2018

Abstract

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.

Keywords: Autoregression, Diffusion, Kurtosis, Stochastic unit root, Time-varying coefficients

JEL Classification: C22

Suggested Citation

Lieberman, Offer and Phillips, Peter C. B., Understanding Temporal Aggregation Effects on Kurtosis in Financial Indices (June 17, 2018). Cowles Foundation Discussion Paper No. 2151, Available at SSRN: https://ssrn.com/abstract=3299494 or http://dx.doi.org/10.2139/ssrn.3299494

Offer Lieberman

Technion-Israel Institute of Technology - The William Davidson Faculty of Industrial Engineering & Management ( email )

Haifa 32000
Israel
973 4 8294438 (Phone)
972 4 8235194 (Fax)

Peter C. B. Phillips (Contact Author)

University of Auckland Business School ( email )

12 Grafton Rd
Private Bag 92019
Auckland, 1010
New Zealand
+64 9 373 7599 x7596 (Phone)

Yale University - Cowles Foundation ( email )

Box 208281
New Haven, CT 06520-8281
United States
203-432-3695 (Phone)
203-432-5429 (Fax)

Singapore Management University - School of Economics

90 Stamford Road
178903
Singapore

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