Some differences in the rates of convergence of the sample covariance
and covariation functions
by Colin M. Gallagher and Toshinori Okuyama.
Abstract:
We compare the rate of convergence of the distribution
functions of the sample covariance and covariation functions for
time series which may be heavy tailed.
A Berry-Essen type bound on the rate of distributional convergence
for the covariation is given.
Since there is no known bound for the sample covariance in the
heavy tailed case, the rates are compared using simulated data.
If the process is symmetric stable, the sample covariation has
an exact stable distribution, while the sample covariance appears to
converge very slowly to its asymptotic distribution.
Key Words:
Time series, Dependence, Sampling distribution
Authors:
Colin M. Gallagher, cgallag@clemson.edu
Toshinori Okuyama, toshi@zoo.ufl.edu
Editor:
Roman Rozanski,rozanski@neyman.im.pwr.wroc.pl
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