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A central limit theorem for self-normalized sums of a linear process

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  • Juodis, Mindaugas
  • Rackauskas, Alfredas

Abstract

Let be a linear process, where and [var epsilon]t, t[set membership, variant]Z, are i.i.d. r.v.'s in the domain of attraction of a normal law with zero mean and possibly infinite variance. We prove a central limit theorem for self-normalized sums where is a sum of squares of block-sums of size m, as m and the number of blocks N=n/m tend to infinity.

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Bibliographic Info

Article provided by Elsevier in its journal Statistics & Probability Letters.

Volume (Year): 77 (2007)
Issue (Month): 15 (September)
Pages: 1535-1541

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Handle: RePEc:eee:stapro:v:77:y:2007:i:15:p:1535-1541

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Keywords: Linear process Normal law Self-normalization;

References

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  1. Beveridge, Stephen & Nelson, Charles R., 1981. "A new approach to decomposition of economic time series into permanent and transitory components with particular attention to measurement of the `business cycle'," Journal of Monetary Economics, Elsevier, vol. 7(2), pages 151-174.
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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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