Abstract
For $j=1,\rm dots,J$, let $K_j:\mathbb{R}\to\mathbb{R}$ be measurable bounded functions and $X_{n,j} = \int_\mathbb{R}a_j(n-c_jx)M(\rm dx)$, $n\ge 1$, be $\alphapha$-stable moving averages where $\alphapha\in(0,2)$, $c_j>0$ for $j=1,\rm dots,J$, and $M(\rm dx)$ is an $\alphapha$-stable random measure on $\mathbb{R}$ with the Lebesgue control measure and skewness intensity $Berry--Esseen boundsta\in[-1,1]$. We provide conditions on the functions $a_j$ and $K_j$, $j=1,\rm dots,J$, for the normalized partial sums vector $ N_j^{-1/2} \sum_{n=1}^{N_j} (K_j(X_{j,n})-\rm EK_j (X_{j,n}))$, $j=1,\rm dots,J$, to be asymptotically normal as $N_j\to\infty$. This extends a result established by Tailen Hsing in the context of causal moving averages with discrete-time stable innovations. We also consider the case of moving averages with innovations that are in the stable domain of attraction.
Citation
Vladas Pipiras. Murad S. Taqqu. "Central limit theorems for partial sums of bounded functionals of infinite-variance\\moving averages." Bernoulli 9 (5) 833 - 855, October 2003. https://doi.org/10.3150/bj/1066418880
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