Sample autocovariances of long-memory time series

Details Sample autocovariances of long-memory time series Sample autocovariances of long-memory time series

2008-05-14

arxiv.org/abs/0805.2029v1

Bernoulli 2008, Vol. 14, No. 2, 405-418

Mathematics

Statistics Theory

Published in at http://dx.doi.org/10.3150/07-BEJ113 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statisti

Scientific paper

10.3150/07-BEJ113

We find the asymptotic distribution of the sample autocovariances of long-memory processes in cases of finite and infinite fourth moment. Depending on the interplay of assumptions on moments and the intensity of dependence, there are three types of convergence rates and limit distributions. In particular, a normal approximation with the standard rate does not always hold in practically relevant cases.

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