 Convergence rates in the central limit theorem for means of autoregressive and moving average sequencesPeter Hall Stochastic Processes and their Applications, 1992, vol. 43, issue 1, 115-131 Abstract: 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. Keywords: autoregression; central; limit; theorem; covariance; function; moving; average; rate; of; convergence; regular; variation (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:43:y:1992:i:1:p:115-131 Ordering information: This journal article can be ordered from Access Statistics for this article Stochastic Processes and their Applications is currently edited by T. Mikosch More articles in Stochastic Processes and their Applications from Elsevier |
Is your work missing from RePEc? Here is how to contribute.
Questions or problems? Check the EconPapers FAQ or send mail to .
EconPapers is hosted by the
School of Business at Örebro University.