NEGATIVE POWERS OF INTEGRATED PROCESSES
推导了积分过程绝对值经负幂次变换后重新标度和的极限分布,以及仅考虑积分过程正值时类似统计量的极限分布,发现极限行为由最接近零的值决定。
This paper derives the limit distribution of the rescaled sum of the absolute value of an integrated process with continuously distributed innovations raised to a negative power less than $-$ 1, and of the analogous statistic that is obtained using the same function of an integrated process but only considering positive values of the integrated process. We show that the limit behavior of this statistic is determined by the values of the integrated process that are closest to 0, and find the limit behavior of the values of the integrated process that are closest to 0.