Predictive And Successful Indicators by John F. Ehlers, PhD
Distortions And Noise
Have you ever thought about how the high-to-low
price swings increase as the time interval increases
on a chart? This tends to create more noise and
distorts indicators. Here are a couple of filters you
can incorporate into your trading system to smooth
data and remove indicator distortions.
Indicators are typically constructed from filters
of one kind or another. Since the price data basically
constitutes a stochastic process, and since
the filters can only use historical data and have no
insight into future data, there is no such thing as a truly
predictive indicator. Predictions are usually made by
other techniques such as extrapolating a trendline,
cross-correlations such as volume leads price, or in
context with another filter such as a divergence. All
of these techniques are anecdotal.
In this article, I will show you how to carefully craft
novel filters to conquer the vagaries of market data,
and how to combine them into advanced indicators.
Then I will demonstrate how even advanced indicators
fail if they are used in the conventional way. Then,
using measured probability density functions, I will
show how to make the indicators predictive with a
high probability of success.
Market data is noisy. The systemic noise arises from
hundreds, if not thousands, of traders placing trades
nearly simultaneously that each trader, for a variety
of reasons, thinks will result in profits. In addition, market data is sampled data rather than continuous
data; that is, there is only one data point on the close of
each day when using daily data. Even if you average
in the high & low prices, there still is only one sample
per day. Of course, you can change the sample rate
using intraday data, but you are still using sampled
data. The result of using sampled data is that there is
substantial aliasing noise several octaves below the
Nyquist frequency. If you prefer, you can think of
this other kind of noise as autocorrelation noise. For
daily data, the period of the Nyquist frequency is a
two-bar cycle. One octave lower is a four-bar cycle,
and one more octave lower is an eight-bar cycle.
Aliasing noise swamps the signal for these shorter
cycle periods, and the only thing that can be done is
to not even try to use cycle periods where the aliasing
noise swamps the signal amplitude.
Aliasing noise is also larger than the signal amplitude
at even longer cycle periods, but the frequency
separation enables filters to reduce or nearly remove
the effects of aliasing noise. Simple moving averages
(SMA) or exponential moving averages (EMA) are
often used to smooth the data in an attempt to reduce
aliasing noise. The problem with using an SMA or
EMA is that they are not efficient filters. The only
way to get more smoothing is to increase the length
of the moving average, which introduces more lag
into the filter.