Stocks & Commodities V. 32:1 (16-25): Predictive And Successful Indicators by John F. Ehlers, PhD

Stocks & Commodities V. 32:1 (16-25): Predictive And Successful Indicators by John F. Ehlers, PhD
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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.

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