Of Trends And Random Walks
by E. Michael Poulos
M y distrust of the current crop of technical indicators that use fixed-length lookback intervals, with
no attempt to use a price-time model, motivated me to do some research into the subject. For example,
one sees chart services publishing a nine-day stochastic and/or relative strength indicator. A variety of
other indicators using moving averages or the difference between moving averages also use fixed lengths.
But there simply is no justification for using nine (or any other fixed number of days) as some sort of
The first six days of Figure 1, part a, have exactly the same moving average value as the first six days of
Figure 1, part b. The close of the seventh day, X, is exactly the same value in both cases. Thus, this kind
of indicator would yield exactly the same number for two very different market conditions. The problem
is not only the fixed-length lookback; the smoothing effect of the moving average destroys all
information about the shape of the market movement. An exponential moving average would do a little
better here, but it too would lose far too much shape information.
The five-day moving average (MA) of Figure 1, part c, is equal to the five-day moving average of Figure
1, part d. The eight-day moving averages of the two are also equal. They would therefore show exactly
the same differences of MAs for two very different price movements. The possibility of an uptrend
indication in one case and downtrend in the other during the last five days is completely lost. The major
problem at this point is loss of shape information.
In Figure 1, parts e and f, the sum of the upclose changes are equal and the sum of the downclose changes
are equal. The RSI calculation would show the same neutral indication in both cases. Not only do the two
cases differ dramatically, their last five days might be indicative of a strong trend, one down and the other