CFDP 2151

Understanding Temporal Aggregation Effects on Kurtosis in Financial Indices

Author(s): 

Publication Date: June 2018

Pages: 39

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 Codes: C22

JEL Classification Codes: C22