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In this paper, some results on complete moment convergence of moving average process generated by  m -WOD random variables are established. The results improve and extend some corresponding ones in the literature. As corollaries, two new results on Marcinkiewicz-Zygmund type strong law of large numbers are established for moving average processes generated by  m -WOD random variables and respectively,  m -END random variables.

Complete moment convergence for moving average process based on m -WOD random variables