We propose and study a new frequency-domain procedure for characterizing and comparing large sets of long time series. Instead of using all the information available from data, which would be computationally very expensive, we propose some regularization rules in order to select and summarize the most relevant information for clustering purposes. Essentially, we suggest to use a fragmented periodogram computed around the driving cyclical components of interest and to compare the various estimates. This procedure is computationally simple, but able to condense relevant information of the time series. A simulation exercise shows that the smoothed fragmented periodogram works in general better than the non-smoothed one and not worse than the complete periodogram for medium to large sample sizes. We illustrate this procedure in a study of the evolution of several stock markets indices. We further show the effect of recent financial crises over these indices behaviour.

中文翻译：

---

大数据时间序列聚类的分段周期图方法

我们提出并研究了一种新的频域过程，用于表征和比较大量的长时间序列。代替使用从数据中获得的所有信息（这在计算上非常昂贵），我们提出一些正则化规则，以便为聚类目的选择和汇总最相关的信息。本质上，我们建议使用围绕感兴趣的驾驶周期性分量计算的分段周期图，并比较各种估计。该过程在计算上很简单，但是能够压缩时间序列的相关信息。仿真实验表明，对于中型到大型样本，平滑的片段化周期图通常比非平滑化的周期图更好，并且不比完整的周期图差。我们在研究几个股票市场指数的演变过程中说明了此过程。我们进一步展示了最近的金融危机对这些指数行为的影响。