V13:06: (247-251):Optimum Predictive Filters by John F. Ehlers
The optimum predictive filter is the difference between a technical indicator, such as the relative strength indicator or stochastics, and its exponential moving
average. Here, we describe it, how to generate it, and how it can be used. It cannot be used in all market conditions - but carefully observing when it can be
used can make it a valuable weapon in your technical arsenal.
Technical analysis is reactive to market activity. The indicators we develop are largely generated to note the
expected price direction. The predictive nature of these indicators is based on our experience, so the expectation is that if a particular action occurred previously, it will occur again. However, none of the indicators are truly predictive in the scientific sense.
Here, we will examine a predictive filter, how to generate it, and most important, the conditions under which the filter can be most effectively used. Like all technical indicators, the optimum predictive filter cannot be used universally in all market conditions. Observing those conditions where it can be used, however, can make the filter a valuable tool in your technical toolbox.
WHAT IT IS
An optimum predictive filter is simply the difference between the original indicator and its exponential moving average. It really is that simple! While the implementation is simple, however, the derivation is considerably more complex.
Having defined an optimum predictive filter, we must specify the conditions for that filter to be valid. First, the
amplitude swings of the original indicator must be limited, and second, the probability of the indicator passing through its zero value must satisfy a Poisson probability distribution. Both conditions are easy to satisfy.