Limiting behaviour of moving average processes under
-mixing assumption
Abstract
Let
be a doubly infinite sequence of identically distributed
-mixing random variables,
an absolutely summable sequence of real numbers. In this paper, we prove the complete convergence and Marcinkiewicz-Zygmund strong law of large numbers for the partial sums of the moving average processes
.
![\{Y_i, -\infty<i<\infty\}](http://212.189.136.205/plugins/generic/latexRender/cache/dade0db0e0a50d016f14145e77e83978.png)
![\rho](http://212.189.136.205/plugins/generic/latexRender/cache/d2606be4e0cd2c9a6179c8f2e3547a85.png)
![\{a_i,-\infty<i< \infty\}](http://212.189.136.205/plugins/generic/latexRender/cache/0317e82325338ce32b440cf0b2082535.png)
![\{\sum\limits^\infty_{i=-\infty}a_i Y_{i+n},n\geq1\}](http://212.189.136.205/plugins/generic/latexRender/cache/66e8f3c1738b0ebe7bd8d4b95d3f3771.png)
DOI Code:
10.1285/i15900932v30n1p17
Keywords:
moving average; Ï?-mixing; complete convergence; Marcinkiewicz-Zygmund strong laws of large numbers
moving average; Ï?-mixing; complete convergence; Marcinkiewicz-Zygmund strong laws of large numbers
Classification:
60F15
Full Text: PDF