Bianchi Sergio, Frezza Massimiliano
Department of Finance and Risk Engineering, Tandon School of Engineering, New York University, New York 11201, USA.
Department of Economics and Law, University of Cassino and Southern Lazio (UCLAM), Cassino, 03043, Italy.
Chaos. 2017 Jul;27(7):071102. doi: 10.1063/1.4987150.
The last systemic financial crisis has reawakened the debate on the efficient nature of financial markets, traditionally described as semimartingales. The standard approaches to endow the general notion of efficiency of an empirical content turned out to be somewhat inconclusive and misleading. We propose a topological-based approach to quantify the informational efficiency of a financial time series. The idea is to measure the efficiency by means of the pointwise regularity of a (stochastic) function, given that the signature of a martingale is that its pointwise regularity equals 12. We provide estimates for real financial time series and investigate their (in)efficient behavior by comparing three main stock indexes.
上一次系统性金融危机重新引发了关于金融市场有效性质的辩论，传统上金融市场被描述为半鞅。事实证明，赋予实证内容有效概念的标准方法在某种程度上没有定论且具有误导性。我们提出一种基于拓扑的方法来量化金融时间序列的信息效率。其思路是通过一个（随机）函数的逐点正则性来衡量效率，因为鞅的特征是其逐点正则性等于1/2。我们对实际金融时间序列进行了估计，并通过比较三个主要股票指数来研究它们的（无）效行为。
