Extremes of Some Sub‐Sampled Time Series
研究了固定间隔子采样对线性过程极值性质的影响，用点过程方法证明收敛定理，给出子采样序列最大值的极限行为，并与原序列比较，对金融和环境监测有参考价值。
Let X k be a stationary time series and y k = X kM be the sub‐sampled series corresponding to a fixed systematic sampling interval M > 1. In this paper, we use a point process approach to study the effect of the sub sampling on the extremal properties of Y k when X k is a linear process with heavy‐tailed innovations. We prove complete point process convergence theorems which enable us to give in detail the weak limiting behaviour of maxima of the sub‐sampled process and to compare it with that of the original process. The results both exemplify the findings of a study by Robinson and Tawn (2000 ) and offer more precise details for the class of linear models. Motivation comes from the comparison of schemes for monitoring financial and environmental processes.