Some limit theorems on stationary processes with long-range dependence
The paper provides central limit theorems on multivariate stationary processes with long-range dependence as a natural extension of the corresponding theory on short-range dependent processes. In order to establish those theorems, the paper imposes weak assumptions on conditional moments of innovation processes, dispensing with the usual assumptions of exact Martingale difference or the contemporaneously transformed Gaussianity.
KeywordsSpectral Density Limit Theorem Central Limit Theorem Innovation Process Schwartz Inequality
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