Quantitative Analysis  |  MAR 2007

Trading Systems And Fractals by Radha Panini

Stocks & Commodities V. 25:3 (36-42): Trading Systems And Fractals by Radha Panini In the second part of this series, we look at the application of fractals to a few well-known trading systems. There have been many applications of fractal methods to trading, the most popular of which has been an indicator based on the fractal dimension of a time series. The fractal dimension index (FDI) can be used as a filter to identify trending compared with trading range markets. Other indicators, like fractal–based adaptive moving averages, have also been proposed. The idea behind such moving averages is to adapt to the randomness of a price series. If the price is more random (trading in a range) as indicated by the fractal dimension value, the moving average is slower, leading to fewer whipsaws. In a less random market (trending), however, the moving average is faster, leading to prompt entries and exits. APPLYING THE FDI In this article, we focus on the FDI and its application to trading systems. The FDI measures the fractal dimension of a price series. Its value ranges between 1 and 2. A value less than 1.5 (a Hurst exponent greater than 0.5) indicates that the price series is persistent, or that the market is trending. On the other hand, a value greater than 1.5 indicates the series is antipersistent or that the market is trading in a range. Figure 1 shows the FDI for IBM for the period 1997–99. The FDI lies mainly above 1.5 when the prices are in a trading range (for example, between September 1997 and April 1998) and falls below 1.5 when prices are trending (for example, between October 1998 and February 1999).

by Radha Panini