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PRECISE ASYMPTOTICS OF MOVING AVERAGE PROCESS UNDER ?-MIXING ASSUMPTION

  • Li, Jie
  • Received : 2010.09.25
  • Published : 2012.03.01

Abstract

In the paper by Liu and Lin (Statist. Probab. Lett. 76 (2006), no. 16, 1787-1799), a new kind of precise asymptotics in the law of large numbers for the sequence of i.i.d. random variables, which includes complete convergence as a special case, was studied. This paper is devoted to the study of this new kind of precise asymptotics in the law of large numbers for moving average process under $\phi$-mixing assumption and some results of Liu and Lin [6] are extended to such moving average process.

Keywords

complete moment convergence;moving average;$\phi$-mixing;precise asymptotics

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Cited by

  1. Precise asymptotics of complete moment convergence on moving average vol.28, pp.12, 2012, https://doi.org/10.1007/s10114-012-0355-1