Convergence rates in the central limit theorem for means of autoregressive and moving average sequences
Let X denote the mean of a consecutive sequence of length n from an autoregression or moving average process. Suppose the covariance function of the process is regularly varying with exponent -[alpha], where [alpha] [greater-or-equal, slanted] 0. We show that the rate of convergence in a central limit theorem for X is identical to that in the central limit theorem for the mean of n independent innovations, if and only if [alpha] [greater-or-equal, slanted] 0. Strikingly, the convergence rate when [alpha] = 0 can be faster than in the case of the independent sequence; it can never be slower. Furthermore, the convergence rate is fastest in the case of strongest dependence. This result is established in two ways: firstly by developing an Edgeworth expansion under the condition of finite third moment of innovations, and secondly by deriving the precise convergence rate in the central limit theorem without an assumption of finite third moment.
Year of publication: |
1992
|
---|---|
Authors: | Hall, Peter |
Published in: |
Stochastic Processes and their Applications. - Elsevier, ISSN 0304-4149. - Vol. 43.1992, 1, p. 115-131
|
Publisher: |
Elsevier |
Keywords: | autoregression central limit theorem covariance function moving average rate of convergence regular variation |
Saved in:
Online Resource
Saved in favorites
Similar items by person
-
Technopoles of the world : the making of 21st century industrial complexes
Castells, Manuel, (1994)
-
Hall, Peter, (1994)
-
Estimating a bivariate density when there are extra data on one or both components
Hall, Peter, (2005)
- More ...