Random Fractals and the Stock Market

Surrogates of the Stock Market - Trading Time Example 1

Price and Trading Time Graph and Difference

On the left we see the 8th iterate sampled at 3128 equal time steps.
On the right is the graph of successive differences.
Finally we see the graphs of price vs clock time differences and price vs trading time differences, plotted on the same scale.
Note the conversion to trading time has removed the large outliers of the difference graph in clock time.
This conversion to trading time has an interesting interpretation.
The price vs trading time difference plot has none of the large jumps we see in the price vs clock time difference plot.
In fact, the price vs trading time difference plot looks much more like a fractional Brownian motion difference plot.
The conversion from price vs clock time to price vs trading time absorbs the large jumps into the (multifractal) time conversion graph, and makes more visible the dependence structure.

Return to Example 1.