We study the intraday behaviour of the statistical moments of the trading volume of the blue chip equities that composed the Dow Jones Industrial Average index between 2003 and 2014. By splitting that time interval into semesters, we provide a quantitative account of the nonstationary nature of the intraday statistical properties as well. Explicitly, we prove the well-known ∪-shape exhibited by the average trading volume—as well as the volatility of the price fluctuations—experienced a significant change from 2008 (the year of the “subprime” financial crisis) onwards. That has resulted in a faster relaxation after the market opening and relates to a consistent decrease in the convexity of the average trading volume intraday profile. Simultaneously, the last part of the session has become steeper as well, a modification that is likely to have been triggered by the new short-selling rules that were introduced in 2007 by the Securities and Exchange Commission. The combination of both results reveals that the ∪ has been turning into a ⊔. Additionally, the analysis of higher-order cumulants—namely the skewness and the kurtosis—shows that the morning and the afternoon parts of the trading session are each clearly associated with different statistical features and hence dynamical rules. Concretely, we claim that the large initial trading volume is due to wayward stocks whereas the large volume during the last part of the session hinges on a cohesive increase of the trading volume. That dissimilarity between the two parts of the trading session is stressed in periods of higher uproar in the market.
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.
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