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Laws of large numbers and central limit theorems for linear processes. (Chinese. English summary) Zbl 1091.60503

Summary: Let \(\{X_t\}\) be a linear process: \(X_t= \sum_{j=0}^\infty c_j \varepsilon_{t-j}\), here \(\{c_j\}\) is a nonrandom constant sequence, \(\{\varepsilon_i,{\mathcal F}_i\}\) is an adapted martingale difference sequence, \(\sum_{j=0}^\infty c_j^2 E\varepsilon_{t-j}^2< \infty\) for \(t=1,2,\dots\). We obtain laws of large numbers and central limit theorems of linear processes by using the Beveridge-Nelson decomposition about linear processes, we generalize and improve the corresponding results of P. C. B. Phillips and V. Solo [Ann. Stat. 20, No. 2, 971–1001 (1992; Zbl 0759.60021)].

MSC:

60F05 Central limit and other weak theorems

Citations:

Zbl 0759.60021
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