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Stochastics is the analysis of an index or set of data relative to its range over a time window. Very simply we find the range of the variable over the time window and then plot the current index value as a percent of the range. Figure 5 illustrates the standard 5-day stochastic "slow" curves.

Standard stochastics analysis (such as on the Dow Jones Industrial Average) uses the theoretical high and theoretical low over the time window to calculate the range. The raw curve (called the %K line) is smoothed to produce the %D line and the %D line is smoothed to produce what I call the %E line. (See "Using Stochastics," S&C, July 1987.) The curves can theoretically vary between 0% and 100%, but typically vary between 30% and 70%. Crossing the %D and %E lines at the upper and lower extremes signals exit and entry.

For SASI stochastics, I make use of the В±3 sigma limits. In Figure 6, I used the last sigma limits and the last index value to calculate %K. The last sigma values are used because they already statistically represent the data variation over the time window. The calculations are:

A = I - (-3 sigma limit)

B = +3 sigma limit - (-3 sigma limit)

%K = 100(A Вё B)

The %D line is a 0.35 exponential smoothing of %K line and %E line is a 0.35 exponential smoothing of the %D line. These values were picked empirically. Sensitivity is varied as for SASITOP by exponentially smoothing the index under evaluation before doing statistical calculations.

At short time windows and moderately low sensitivity (0.08) an interesting effect occurs: When a market trend is under way the %D and %E lines will flatten out at the 70% or 30% level and remain there for the duration of the trend.

This effect makes it relatively easy to stay with a trend for the full duration and enter or exit within a few days of major turning points. An empirical trigger value can be picked based on your individual trading preference. When the %D line crosses this level it is the entry or exit signal.

Figure 7 shows SASI variable sensitivity stochastics based on В±3 sigma limits and operating on the Technical Index. The exponential smoothing sensitivity is set low at 0.05 to emphasize the effect. A trigger level for exit at 69% and a trigger level for entry at 31% is depicted. Note how using this technique would have kept you either in (long) or out (short) for the lion's share of the major trends.

The flattening effect of the %D and %E lines diminishes as the time window is increased. Experience suggests that time windows of five or six days are best for this flattening effect.

Another benefit of the overall sigma limit technique is that it makes it very easy to set up a spreadsheet like Lotus 1-2-3 so that any index or set of data can be quickly evaluated over a range of sensitivities.