英文标题：
《A memory-based method to select the number of relevant components in
Principal Component Analysis》
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作者：
Anshul Verma and Pierpaolo Vivo and Tiziana Di Matteo
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最新提交年份：
2019
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英文摘要：
We propose a new data-driven method to select the optimal number of relevant components in Principal Component Analysis (PCA). This new method applies to correlation matrices whose time autocorrelation function decays more slowly than an exponential, giving rise to long memory effects. In comparison with other available methods present in the literature, our procedure does not rely on subjective evaluations and is computationally inexpensive. The underlying basic idea is to use a suitable factor model to analyse the residual memory after sequentially removing more and more components, and stopping the process when the maximum amount of memory has been accounted for by the retained components. We validate our methodology on both synthetic and real financial data, and find in all cases a clear and computationally superior answer entirely compatible with available heuristic criteria, such as cumulative variance and cross-validation.
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中文摘要：
我们提出了一种新的数据驱动方法来选择主成分分析（PCA）中相关成分的最佳数目。这种新方法适用于时间自相关函数衰减比指数衰减慢的相关矩阵，从而产生长记忆效应。与文献中的其他可用方法相比，我们的方法不依赖于主观评估，并且计算成本较低。其基本思想是使用一个合适的因子模型来分析顺序移除越来越多的组件后的剩余内存，并在保留的组件占用了最大内存量时停止该过程。我们在合成和真实财务数据上验证了我们的方法，并发现在所有情况下，都有一个清晰且计算上优越的答案，完全符合可用的启发式标准，如累积方差和交叉验证。
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分类信息：

一级分类：Quantitative Finance 数量金融学
二级分类：Statistical Finance 统计金融
分类描述：Statistical, econometric and econophysics analyses with applications to financial markets and economic data
统计、计量经济学和经济物理学分析及其在金融市场和经济数据中的应用
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