[blackcat] L2 Ehlers Phase Accumulator Cycle Period Measurer

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Level: 2

Background

John F. Ehlers introuced Phase Accumulation technique of cycle period measurement in his "Rocket Science for Traders" chapter 7. It is perhaps the easiest to comprehend. In this technique, John Ehlers measures the phase at each sample by taking the arctangent of the ratio of the Quadrature component to the In-phase component. A delta phase is generated by taking the difference of the phase between successive samples. At each sample Dr . Ehlers then looks backward, adding up the delta phases. When the sum of the delta phases reaches 360 degrees (2*pi in tradingview), we must have passed through one full cycle, on average. The process is repeated for each new sample.

Function
blackcat L2 Ehlers Phase Accumulator Cycle Period Measurer is used to measure Dominant Cycle (DC). This is one of John Ehlers three major methods to measure DC. The Phase Accumulation method of cycle measurement always uses one full cycle’s worth of historical data. This is both an advantage and disadvantage. The advantage is the lag in obtaining the answer scales directly with the cycle period. That is, the measurement of a short cycle period has less lag than the measurement of a longer cycle period. However, the number of samples used in making the measurement means the averaging period is variable with cycle period. Longer averaging reduces the noise level compared to the signal. Therefore, shorter cycle periods necessarily have a higher output Signal-to-Noise Ratio ( SNR ).

Key Signal

Smooth --> 4 bar WMA w/ 1 bar lag
Detrender --> The amplitude response of a minimum-length HT can be improved by adjusting the filter coefficients by
trial and error. HT does not allow DC component at zero frequency for transformation. So, Detrender is used to remove DC component/ trend component.
Q1 --> Quadrature phase signal
I1 --> In-phase signal
Period --> Dominant Cycle in bars

Pros and Cons

100% John F. Ehlers definition translation of original work, even variable names are the same. This help readers who would like to use pine to read his book. If you had read his works, then you will be quite familiar with my code style.

Remarks

The 2nd script for Blackcat1402 John F. Ehlers Week publication.

Readme

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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Open-source script

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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