Some Limit Theory for the Self-normalised Periodogram of Stable Processes

Some Limit Theory for the Self-normalised Periodogram of Stable Processes
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稳定过程自归一化周期图的一些极限理论

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发表时间：
1994
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通讯作者：
T. Mikosch
T. Mikosch
中科院分区：
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文献类型：
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作者：
C. Klüppelberg;T. Mikosch

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设X(T)=Sigma(J)(无穷)=(-无穷)psi(J)Z(t-j)是基于I.I.D.的离散移动平均过程。具有公共分布函数的随机变量(Z(T)，)具有来自正态吸引域的p-稳定律(0&lt；p小于或等于2)。我们证明了自归一化周期图[GRAPJICS]的弱收敛。此外，我们还证明了($)在条形I-n，(X)(Lambda)上的光滑化形式给出了与p无关的任何p epsilon(0，2)的归一化传递函数的一致估计。
Let X(t) = Sigma(j)(infinity) = (-infinity) psi(j)Z(t-j) be a discrete moving average process based on i.i.d. random variables (Z(t),)(t epsilon Z) with common distribution function from the domain of normal attraction of a p-stable law (0 <p less than or equal to 2). We prove weak convergence of the self-normalised periodogram [GRAPJICS] Furthermore, we show that smoothed versions of ($) over bar I-n,(X)(lambda) provide consistent estimates for the normalised transfer function for any p epsilon (0, 2] independent of p.