In this article, I am presenting
elementary Statistical Analysis of Stocks and Indices (SASI) in an index, three
new indicators (SASITOP, SASIBOT and sigma limits) plus variable-sensitivity
stochastics based on statistical analysis. SASITOP is very similar to
stochastics but uses plus and minus variance (sigma) limits in place of the
high and low over the time window. The data is modified for sharper
sensitivity. Because SASITOP and SASIBOT are the reciprocal of each other, I
will concentrate only on SASITOP in this article and apply it to the Technical
Index which measures overall market breadth (see Stocks & Commodities,
January 1989) although it may be applied to any index or set of data.
To generate SASITOP:
1. Calculate the statistical sample
variation s2. For a finite population, s2 is mathematically described by:
where X represents the values in your
time series and n is number of observations
Don't panic. Use a spreadsheet like
Lotus 1-2-3 which has a built in variance function. The Lotus 1-2-3 variance
function has to be modified: s2m = s2[n/(n-1)] to account for a finite
population (where n = the time window). Some spreadsheets such as Excel have
this modification built in to the variance (VAR) function.
2. Next calculate the standard
deviation, S, which is the square root of the variation: sm sm = 2
3. Calculate the index's 5-day
average (AVG) for the data over the chosen time window.
4. Calculate the +3 sigma limit as:
(3sm)+AVG; the -3 sigma limit is: AVG-(3s m).
Figure 1 depicts the В±3 sigma limits around an index.
Value A is the difference between the last +3 sigma value and the last index value,
I. That is, A = +3 sigma -I and B=I- (-3 sigma).
The SASITOP value is: BВёA. Just like moving average
calculations, you continue sliding the time window and calculating a new
SASITOP value for each time increment.
Figure 2 is a plot of SASITOP on
the Technical Index in which the SASITOP value has been adjusted to fit the
graph. When SASITOP turns in the region of 1,100-1,300 and heads south the
investor should be alert. By looking at prior market data, the noise level can
be estimated as in Figure 2. SASITOP signals an exit when it breaks below the noise level (points
A, B, C and D).
I found by empirical
experimentation after the sigma limit calculations were complete that if the
index value, I, is replaced with a smoothed value, Is, the SASITOP value more
or less approaches a constant if the smoothing was approximately equal to
one-half the time window. All of the SASITOP figures in this article have this
modification. The overall SASITOP sensitivity is varied by first exponentially
smoothing the index under evaluation.
SASITOP calculations are
then done on the smoothed index. Figure 2 is at a low sensitivity of 0.05 and
В Figure 3 is at a sensitivity of 1.0 (no smoothing) for very
active trading. The sensitivity can be set to accommodate anything from daily
trading to intermediate-term investing.
Figure 4 is a magnified view of Figure 3 showing the exit
signals. When the SASITOP indicator turns and forms a top (points A through H),
this is the signal to exit or go short. At this sensitivity (1.0), you are
going to get knee-jerked fairly often (points F and G). If you had the courage
to hold your position for several days you would have been rewarded.
Exponential smoothing revisited
One exponential smoothing formula
is:
Last + a(Ic - Last)
where Last is the previous
exponential calculation and Ic is the current index value. The initial value
for Last is the current index value. Sensitivity is changed by changing the
value of a (alpha). A useful range for a is 0.05 to 1.0.
Stochastic & RSI
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