Base description

The basic rules for the presentation

A short reminder can be given here, for example about the meaning for the axis.
The left figure displays some data with the same visualization for all time series: the ranges for the axes and the color choices are identical. For the two dimensional color plots, the color mapping is dark blue (strongly negative), turquoise (slightly negative), white (around zero), yellow (slightly positive), red (strongly positive).

Theses figures allow for a direct comparison between time series.

The right figure displays the same data, but with automatically adjusted axes and colors. For the two dimensional color plots, the color mapping is dark blue (small), turquoise, green (mid-range), yellow, red (large).

These figures allow to display the data optimally, regardless of the differences between processes and empirical data.

The presentation in the descriptions pages

The presentation is similar in the description pages
On the left side, a typical figure is given for an empirical time series. The figure is explained on the right side, including the formula used for the computations and the meaning for the axes.

In the subsequent paragraphs, the generic features observed in the empirical data are pointed out. For example, the fat tails are noticed on the probability density of the returns. The discussion stays at a generic level, with features that are present in most or all empirical time series. The actual properties may differ on some of them, and the reader should consult the specific pages for each empirical time series.

Of course, the properties of processes can be quite different from the empirical one.