Publication Date: June 2018
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: C22See CFDP Version(s): CFDP 1769