Intraday seasonalities and nonstationarity of trading volume in financial markets: Collective features

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.本研究借助随机矩阵理论（Random Matrix Theory）与主成分分析（Principal Component Analysis）技术，将我们此前针对金融市场交易量的个体及截面日内统计特征的研究拓展至该金融指标的集体日内特征分析。我们的数据集涵盖2003年至2014年间道琼斯工业平均指数（Dow Jones Industrial Average Index）成分股的交易量数据。通过计算日内时变相关矩阵及其特征值谱，我们发现存在一个主导这些个股交易量集体行为的特征模态，其余特征值均落在随机矩阵理论划定的边界之内，唯有第二大特征值在开盘时段显著高于上界，且在午间过渡阶段亦略高于该边界。考虑到此前针对价格波动的研究已报道至少存在7个显著特征值，且高流动性个股的价格自相关函数接近白噪声，而交易量的自相关函数则会持续超过2小时，即便考虑到埃普斯效应（Epps effect），我们的发现仍与基于上述特征得出的所有预期相悖。此外，交易量集体主导模态的权重具有日内依赖性：随着交易时段推进，该模态的权重不断提升，其单位特征向量也逐渐趋近于均匀向量，这意味着个股交易量的行为同质性显著增强。针对交易量集体特征的非平稳性，我们观察到：2008年金融危机后，相干函数的分布呈现出显著波动的异常形态，这一特性与我们此前个体分析中观察到的平均交易量分布的变化相一致。