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

Colin M. Gallagher,
Toshinori Okuyama,

Editor: Roman Rozanski,

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