时间序列的移动平均值的记录
Records for the moving average of a time series
摘要：
我们调查如何统计的极值和记录时，采取移动平均宽度$p$的一个独立的，同分布的随机变量序列的窗口。一般情况下的渐近分析，证实了三种分布（指数，均匀，幂律与单位指数）的确切结果，证明了一个非常强大的二分法，无论窗口宽度，超指数和次指数分布之间。对于超指数分布的统计记录是渐近不变的移动平均值，有趣的分布相关的校正标度。对于次指数分布，在后期打破记录的概率增加了一个通用因子$R_p$，仅取决于窗口宽度。
英文摘要：
We investigate how the statistics of extremes and records is affected when taking the moving average over a window of width $p$ of a sequence of independent, identically distributed random variables. An asymptotic analysis of the general case, corroborated by exact results for three distributions (exponential, uniform, power-law with unit exponent), evidences a very robust dichotomy, irrespective of the window width, between superexponential and subexponential distributions. For superexponential distributions the statistics of records is asymptotically unchanged by taking the moving average, up to interesting distribution-dependent corrections to scaling. For subexponential distributions the probability of record breaking at late times is increased by a universal factor $R_p$, depending only on the window width.
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