Random Fractals and the Stock Market

Surrogates of the Stock Market - Trading Time Example 2

Because the conversion to trading time is such a powerful tool for unpacking complicated features of time series, we consider another example, the generator with turning points (0.2, 0.7) and (0.6, 0.4).

First, we compute the price and clock time increments, and observe this is not a unifractal generator. Here is the price and clock time graph, along with the graph of first differences and a comparison of relating some large differences to the graph. This is just an illustration, not part of the method of graphing price vs trading time. Next, we find the trading time generator. Here is the trading time and clock time graph, along with the graph of first differences. This is just an illustration, not part of the method of graphing price vs trading time. Now we compute the price and trading time generator. Finally, here is the price and trading time graph, along with the graph of first differences.

Summary:

For large dY in small dt, stretch the time scale for dT - a lot of trading time in a little clock time. For small dY in large dt, compress the time scale for dT - a little trading time in a lot of clock time. The trading time conversion removes long tails by changing the time scale, and keeps the dependence of increments.

Return to Trading Time.