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


  • Juodis, Mindaugas
  • Rackauskas, Alfredas


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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  • Juodis, Mindaugas & Rackauskas, Alfredas, 2007. "A central limit theorem for self-normalized sums of a linear process," Statistics & Probability Letters, Elsevier, vol. 77(15), pages 1535-1541, September.
  • Handle: RePEc:eee:stapro:v:77:y:2007:i:15:p:1535-1541

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    References listed on IDEAS

    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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