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中文摘要：
滑动平均过程常被用于平滑时间序列数据的短期波动和突出它的长期趋势或周期,而ρ-混合相依结构在金融时间序列中广泛存在.本文主要考虑基于ρ-混合序列滑动平均过程.在一些适当矩和含有或不含有最大混合系数率的条件下,通过用ρ-混合序列最大部分和Rosenthal型不等式,证明了基于ρ-混合序列滑动平均过程最大部分和的矩存在性.本文得到的结果改进和推广了以前的一些结果.
英文摘要：
Moving average processes are commonly applied to the time series data set to smooth out its short-term fluctuations and highlight its longer-term trends or cycles. The ρ-mixing dependence is a common assumption in the financial and economic time series. In this paper, we consider the moving average processes based on ρ-mixing sequence. Under some suitable conditions of moments, and with or without maximal correlation coefficient rate, we prove the existence of moments of the maximum of partial sums about moving aver- age processes based on the ρ-mixing sequence by using the Rosenthal-type inequality of maximum partial sums of ρ-mixing sequence. Some well-known results are improved and extended by the proposed result.
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