# [blackcat] L2 Ehlers Autocorrelation Indicator

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Level: 2

Background

John F. Ehlers introduced Autocorrelation Indicator in his "Cycle Analytics for Traders" chapter 8 on 2013.

Function

If we correlate a waveform composed of perfectly random numbers by itself, the correlation will be perfect. However, if we lag one of the data streams by just one bar, the correlation will be dramatically reduced. In a long memory process with normally distributed random numbers the autocorrelation follows the power law.

One of the underlying principles of technical analysis is that market data do not follow this power law of an efficient market, and we therefore can extract information from the partial correlation of the autocorrelation function. For example, assume the data being examined is a perfect sine wave whose period is 20 bars. The autocorrelation with zero lag, averaged over one full period of the sine wave , is unity . That is, the correlation is perfect. Introducing a lag of one bar in the autocorrelation process causes the average correlation to be decreased slightly. Introducing another bar of lag further decreases the average correlation, and so on. That is, until a lag of 10 bars is reached. In this case, the positive alternation of the sine wave is correlated with the negative alternation of the lagged waveform and the negative alternation of the sine wave is correlated with the positive alternation of the lagged waveform, with the result that perfect anticorrelation has been reached. Continued lag increases causes the average correlation to increase until a lag of 20 bars is reached. When the lag is equal to the period of the sine wave waveform, the correlation is again perfect. In this theoretical example, the correlation values as a function of lag vary exactly as a sine wave .

Market data are considerably messier than purely random numbers or perfect sine waves but contain features of both. However, the characteristics that are uncovered by autocorrelation offer unique trading perspectives. Aside from appearing psychedelic, there are two distinct characteristics of the autocorrelation indicator using minimum averaging. First, there is a sharp reversal from red to yellow and from yellow to red at the timing of price reversals for all periods of lag. Second, there is a variation of the thickness of the bars and the number of bars over the vertical range of the indicator as a function of time.

Key Signal

Corr --> Pearson correlation data array

Pros and Cons

I am sorry this script is NOT 100% as original Ehlers works but I modified it accordingly which demostrated with better visual effect.

Remarks

The 47th script for Blackcat1402 John F. Ehlers Week publication.

Courtesy of @RicardoSantos for RGB functions.

In real life, I am a prolific inventor. I have successfully applied for more than 60 international and regional patents in the past 12 years. But in the past two years or so, I have tried to transfer my creativity to the development of trading strategies. Tradingview is the ideal platform for me. I am selecting and contributing some of the hundreds of scripts to publish in Tradingview community. Welcome everyone to interact with me to discuss these interesting pine scripts.

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Versionshinweise: This version update makes tradeoffs between resolution and visual scope.

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Open-source Skript

In true TradingView spirit, the author of this script has published it open-source, so traders can understand and verify it. Cheers to the author! You may use it for free, but reuse of this code in a publication is governed by House Rules. You can favorite it to use it on a chart.

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