Identifying The Character Of Indicators
Divergence Bias
by Giorgos Siligardos, Ph.D.
Did you know that classical momentum and trend indicators have a bias in forming divergences?
One of the most common, elementary concepts in technical analysis is that of momentum. Most books on technical analysis have a reference, a section, or a few paragraphs devoted to it; however, no work has been published discussing whether the various momentum indicators incorporate a bias in forming divergences from the price. Until now.
DEFINITION OF MOMENTUM
If P is the price of an equity and P-n was the price of the same equity
n periods ago, then the momentum concept of n periods can be defined:
or 
It is easy to see that I(n) = 100 * fracMom(n)?100 and that:
which means that I(n) and fracMom(n) are equivalent with respect to divergence via the strictly increasing function f(x) = 100x?100. In addition, J(n) and fracMom(n) are equivalent with respect to divergence via the strictly increasing function:
Therefore, we conclude that I(n), J(n), and fracMom(n) have the same performance with respect to divergence. This means there is no way these indicators can diverge from one another. Moreover, they provide the same diverging signals with price (see Figure 1 as an example). Thus, we shall focus our study on the Mom(n) and fracMom(n) indicators.
Figure 1: Daily chart of the Dow Jones Industrial Average. I(30), J(30), and fracMOM(30) do not diverge one from another and so they simultaneously diverge from the price. There is a similar hold for fracMACD and MACD.
Excerpted from an article originally published in the December 2003 issue of Technical Analysis of STOCKS & COMMODITIES magazine. All rights reserved. © Copyright 2003, Technical Analysis, Inc.
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