arXiv 2207.048672022-07q-fin.STcs.LGq-fin.CPq-fin.RM

股票收益率的Lepto方差

The Lepto-Variance of Stock Returns

Aristotle University（亚里士多德大学）

Vassilis Polimenis

摘要：

回归树（RT）使用特定特征对样本进行排序，并找到从节点到其子节点产生最大方差缩减的分割点。我们的关键观察是，最好使用的因素（在MSE下降方面）总是目标本身，因为这最清楚地区分了目标。因此，使用目标作为分裂因子提供了MSE下降的上限（或残余子MSE的下限）。基于这一观察，我们将目标变量的k位lepto-variance $λk^2$（或等效地，特定深度k处的lepto-variance）定义为不能被深度等于k的任何回归树移除的方差。作为任何特征的上限性能，我们认为$λk^2$是一个有趣的统计概念，与样品的底层结构相关，因为它量化了样品RT的分辨能力。可以使用高达k的深度的RT来解释的最大方差被称为样本k比特宏方差。因此，在任何深度，总样本方差被分解为细方差$λ^2$和宏方差$μ^2$。我们证明了这个概念，通过执行1位和2位RT为基础的瘦结构分析每日IBM股票收益。

英文摘要：

The Regression Tree (RT) sorts the samples using a specific feature and finds the split point that produces the maximum variance reduction from a node to its children. Our key observation is that the best factor to use (in terms of MSE drop) is always the target itself, as this most clearly separates the target. Thus using the target as the splitting factor provides an upper bound on MSE drop (or lower bound on the residual children MSE). Based on this observation, we define the k-bit lepto-variance $λk^2$ of a target variable (or equivalently the lepto-variance at a specific depth k) as the variance that cannot be removed by any regression tree of a depth equal to k. As the upper bound performance for any feature, we believe $λk^2$ to be an interesting statistical concept related to the underlying structure of the sample as it quantifies the resolving power of the RT for the sample. The max variance that may be explained using RTs of depth up to k is called the sample k-bit macro-variance. At any depth, total sample variance is thus decomposed into lepto-variance $λ^2$ and macro-variance $μ^2$. We demonstrate the concept, by performing 1- and 2-bit RT based lepto-structure analysis for daily IBM stock returns.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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英文摘要：

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