Total information flow as a function of time—The prices time series.

<p>Behavior of the total information flow <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0176764#pone.0176764.e012" target="_blank">Eq (6)</a> at different time differences <i>δ</i>, when computed for daily prices rather than returns. Each time window <i>w</i> is 500 days long. The date associated with each <i>w</i> is the middle of the time window considered. The <i>x</i>-axis tick marks correspond to the dates of the first of March each year. No meaningful information can be obtained from this analysis in contrast to the results presented in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0176764#pone.0176764.g001" target="_blank">Fig 1</a>.</p

Information directionality flow.

<p>For each component <i>n</i>, we evaluate the information directionality flow Δ_<i>n</i>, defined in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0176764#pone.0176764.e016" target="_blank">Eq (7)</a>, measuring how much the component has influenced (or has been influenced by) the market. Positive values are associated to lead effects. The horizontal axis refers to the window time index <i>w</i>. The vertical axis refers to the component index. It is interesting to see how strength and directionality of influences become clearer and more emphasized at time of financial crises. A closer look at these values is provided in Figs <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0176764#pone.0176764.g004" target="_blank">4</a> and <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0176764#pone.0176764.g005" target="_blank">5</a>.</p

Total information flow as a function of time.

<p>The behavior of the total information flow , defined in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0176764#pone.0176764.e012" target="_blank">Eq (6)</a>, at different time scales <i>δ</i>. Each time window <i>w</i> is 500 days long. The date associated to each <i>w</i> is the middle of the time window considered. The <i>x</i>-axis tick marks represent the first of March of every year. While at short time scales (less than 3 days) we observe a peak around the two major financial crises of the last decades, this effect fades away as <i>δ</i> increases. Interestingly, the results at <i>δ</i> = 2 carries much more information than those at <i>δ</i> = 1.</p

Network evolution.

<p>Plot of , the information flow in two consecutive time windows, defined in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0176764#pone.0176764.e011" target="_blank">Eq (5)</a>, at time differences <i>δ</i> = 2 and <i>δ</i> = 3. Each time window <i>w</i> is 500 days long. The date associated to each <i>w</i> is the middle of the time window considered. The <i>x</i>-axis tick marks represent the first of March of every year. This quantity measures the evolution of the detected structure of influences. We observe a smooth behavior, meaning that structures in consecutive time windows are similar, except for during crises where more pronounced market readjustment take place.</p

Directionality leaders.

<p>To identify more clearly leading stocks in terms of their effect on others, we present the information of <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0176764#pone.0176764.g003" target="_blank">Fig 3</a>, but focussing on the 30 components with the <i>largest</i> directionality flow values. For the sake of clarity each time tick has been obtained by averaging three consecutive time windows. So we have about 45 different ticks rather than the original 140 time windows.</p

Directionality followers.

<p>To identify more clearly stocks led by the market, we present the information of <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0176764#pone.0176764.g003" target="_blank">Fig 3</a>, but focussing on the 30 components with the <i>smallest</i> directionality flow values. For the sake of clarity each time tick has been obtained by averaging three consecutive time windows. So we have about 45 different ticks rather than the original 140 time windows.</p