The limit behavior of partial sums for short range dependent stationary sequences (with summable autocovariances) and for long range dependent sequences (with autocovariances summing up to infinity) differs in various aspects. We prove central limit theorems for partial sums of subordinated linear processes of arbitrary power rank which are at the border of short and long range dependence.

中文翻译：

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近长程相关从属线性过程的中心极限定理

对于短程相关的平稳序列（具有可求和的自协方差）和长程相关的序列（自协方差总和为无穷大）的部分和的极限行为在各个方面有所不同。我们证明了处于短期和长期依赖边界的任意功率等级的从属线性过程的部分和的中心极限定理。