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.
Highlights
Despite the fact that the state of a financial asset—and the indices composed thereof—is traditionally characterised by the respective price, S(t), and its variation, rΔt(t), with respect to a given period of time, Δt, it is nowadays well-established that the complex nature of a financial system cannot be satisfactorily described by a reduced number of quantities [1,2,3,4]
Taking into consideration that work and the relevance of trading volume in the characterisation of the dynamics of financial markets, in this manuscript, we introduce a comparable analysis of the intraday properties of v
We use the following notation: vi(d, t; s) represents, the 1-minute trading volume of company, i, at the intraday time, t—is defined in a integer number format with t = 0 representing 9:30 in clock time and t = 390 corresponding to 16:00, on the day, d; we take into account the semester, s, to which d belongs because we divide our data into contiguous semesters in order to assess the nonstationarity of the intraday properties
Summary
Despite the fact that the state of a financial asset—and the indices composed thereof—is traditionally characterised by the respective price, S(t), and its (percentual) variation, rΔt(t), with respect to a given period of time, Δt, it is nowadays well-established that the complex nature of a financial system cannot be satisfactorily described by a reduced number of quantities [1,2,3,4] For this reason, as we move up from mainstream mass media towards financial platforms we are by default told about quantities like the volatility, S, and the amount of the asset The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript
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