Graczyk Michelle B, Duarte Queirós Sílvio M
Centro Brasileiro de Pesquisas Físicas, Rio de Janeiro, RJ, Brazil.
National Institute of Science of Technology for Complex Systems, Rio de Janeiro, RJ, Brazil.
PLoS One. 2017 Jul 28;12(7):e0179198. doi: 10.1371/journal.pone.0179198. eCollection 2017.
Employing Random Matrix Theory and Principal Component Analysis techniques, we enlarge our work on the individual and cross-sectional intraday statistical properties of trading volume in financial markets to the study of collective intraday features of that financial observable. Our data consist of the trading volume of the Dow Jones Industrial Average Index components spanning the years between 2003 and 2014. Computing the intraday time dependent correlation matrices and their spectrum of eigenvalues, we show there is a mode ruling the collective behaviour of the trading volume of these stocks whereas the remaining eigenvalues are within the bounds established by random matrix theory, except the second largest eigenvalue which is robustly above the upper bound limit at the opening and slightly above it during the morning-afternoon transition. Taking into account that for price fluctuations it was reported the existence of at least seven significant eigenvalues-and that its autocorrelation function is close to white noise for highly liquid stocks whereas for the trading volume it lasts significantly for more than 2 hours -, our finding goes against any expectation based on those features, even when we take into account the Epps effect. In addition, the weight of the trading volume collective mode is intraday dependent; its value increases as the trading session advances with its eigenversor approaching the uniform vector as well, which corresponds to a soar in the behavioural homogeneity. With respect to the nonstationarity of the collective features of the trading volume we observe that after the financial crisis of 2008 the coherence function shows the emergence of an upset profile with large fluctuations from that year on, a property that concurs with the modification of the average trading volume profile we noted in our previous individual analysis.
运用随机矩阵理论和主成分分析技术，我们将在金融市场中对交易量的个体和横截面日内统计特性的研究扩展到对该金融可观测指标的集体日内特征的研究。我们的数据包括2003年至2014年期间道琼斯工业平均指数成分股的交易量。通过计算日内时间相关矩阵及其特征值谱，我们发现存在一种模式支配着这些股票交易量的集体行为，而其余特征值处于随机矩阵理论所确定的范围内，但第二大特征值在开盘时稳健地高于上限，在上午 - 下午过渡期间略高于上限。考虑到对于价格波动报告存在至少七个显著特征值，并且对于高流动性股票其自相关函数接近白噪声，而对于交易量其持续时间显著超过2小时，我们的发现与基于这些特征的任何预期相悖，即使我们考虑了埃普斯效应。此外，交易量集体模式的权重是日内依赖的；其值随着交易时段的推进而增加，其特征向量也接近均匀向量，这对应于行为同质性的飙升。关于交易量集体特征的非平稳性，我们观察到2008年金融危机后，相干函数显示从那一年起出现了一个波动较大的异常轮廓，这一特性与我们之前个体分析中注意到的平均交易量轮廓的变化一致。
