滑动平均过程误差项局部极值间距离的渐近概率分布
Asymptotic probability distribution of distances between local extrema of error terms of a moving average process
摘要：
考虑移动平均过程MA（q）的误差项x（i），其中x（i）=e（i）+ e（i-1）+.+ e（i-q）和e（i）-独立同分布（i.i.d.）随机变量。如果下列条件成立，则我们将项x（i）识别为局部极大值：x（i-1）< x（i）> x（i+1）。如果局部极大值x（i）之后是下一个局部极大值x（k），则d=k-i是局部极大值之间的距离。距离d（j）本身是随机变量。本文研究距离d（j）的概率分布。特别地，我们证明了对于任何q>0，平均距离E[d（j）]=4，并且渐近方差也等于4。
英文摘要：
Consider error terms x(i) of a moving average process MA(q), where x(i)=e(i) + e(i-1)+...+e(i-q) and e(i) - independent identically distributed (i.i.d.) random variables. We recognize a term x(i) as a local maximum if the following condition holds true: x(i-1) < x(i) > x(i+1). If the local maximum x(i) is followed by the next local maxiumum x(k), then d=k-i is the distance between local maxima. The distances d(j) themselves are random vriables. In this paper we study the probability distribution of distances d(j). Particularly, we show that for any q>0 mean distance E[d(j)]=4 and asymptotically the variance is also equal to 4.
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