Intraday Seasonalities and Nonstationarity of Trading Volume in Financial Markets: Individual and Cross-Sectional Features

Abstract

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.

A multi-scale symmetry analysis of uninterrupted trends returns of daily financial indices

“…Initially, most of the market symmetry or gain/loss asymmetry studies relied on studying the third standardized moment of the price or index variations or other similar measurement. More recently, symmetry of financial variations or related problems has been approached by very ingenious methodologies, as for example, the analysis of the returns distribution of stocks ensembles during crash and rally days [9]; the study of large fluctuation dynamics under time reversal (TR) symmetry (large fluctuations dynamics at daily scale are not TR symmetric, but at the scale of high frequency data they are) [10]; study of the investment horizons distribution [11,12]; empirical analysis of the clustering on the asymmetry properties in financial time series [13]; symmetry break mechanisms [14]; symmetry in trading volume [15]; analysis related to time-scale effects on gain/loss asymmetry in stock indices [16]; the use of the non-extensive formalism of Physics [17], or focusing in searching possible symmetry points of returns [18] and many more interesting empirical and agents modeled studies [19,20].…”

“…For instance, [21,22] have analyzed returns of a large sample of diverse financial indices without finding important symmetry deviations or fully rejecting the symmetry hypothesis. On the other hand, many studies under different conditions and points of view have reported the emergence of asymmetries in the financial returns distribution [9][10][11][12][13][14][15][16][17][18][19][20].…”

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

“…In a previous paper of ours, hereinafter referred to as Paper I [ 11 ], we introduced a broad study over the individual and cross-sectional intraday statistical properties of the trading volume of blue chip equities that composed the Dow Jones Industrial Average with the aiming of going beyond the well-known intraday ∪-shape of the average trading volume, a profile that is also shared by different definitions of the volatility, including the absolute value of the price fluctuations [ 1 , 12 – 16 ]. Paper I showed important features of the trading volume such as the fact the morning (am) and the afternoon (pm) parts of the business day clearly have different dynamical mechanisms of trading.…”