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Limit theorems for self-normalized linear processes

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  • Kulik, Rafal

Abstract

In this article we prove a self-normalized central limit theorem and an invariance principle in the case of strictly stationary linear processes assuming that the i.i.d. random variables {Zt} are in the domain of attraction of the normal law.

Suggested Citation

  • Kulik, Rafal, 2006. "Limit theorems for self-normalized linear processes," Statistics & Probability Letters, Elsevier, vol. 76(18), pages 1947-1953, December.
    • Handle: RePEc:eee:stapro:v:76:y:2006:i:18:p:1947-1953
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    References listed on IDEAS

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    1. Raluca Balan & Kulik, 2005. "Self-Normalized Weak Invariance Principle for Mixing Sequences," RePAd Working Paper Series lrsp-TRS417, Département des sciences administratives, UQO.
    2. Rackauskas, Alfredas & Suquet, Charles, 2001. "Invariance principles for adaptive self-normalized partial sums processes," Stochastic Processes and their Applications, Elsevier, vol. 95(1), pages 63-81, September.
    3. Wang, Qiying & Lin, Yan-Xia & Gulati, Chandra M., 2001. "Asymptotics for moving average processes with dependent innovations," Statistics & Probability Letters, Elsevier, vol. 54(4), pages 347-356, October.
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    Cited by:

    1. Moon, H.J., 2008. "The functional CLT for linear processes generated by mixing random variables with infinite variance," Statistics & Probability Letters, Elsevier, vol. 78(14), pages 2095-2101, October.

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