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I agree with you that the lengths (and amplitudes) vary. When I was using the word "cycle" I did not mean to say the periodicity of the cycles was fixed (the lengths of the waves was fixed).
I do not think I have the correct language for it but I thought the Fournier process decomposed a composite wave into several component waves.
Here is what I am trying to express:
The blue line is the composite, The black line is the dominant cycle/wave, the red line is the secondary cycle/wave:
..........
peace, love and joy to you
.........
Can you help answer these questions from other members on NexusFi?
1. Yes you can post code.
However, it won't be any good to me as I'm not a programmer.
(In case you didn't know ninja trader indicators are written in C.)
Cutting and pasting wouldn't be any good for me time is a big limitation.
2. Detecting turns is what it's "all about" for me. As I mentioned I did download the Corona indicator package and one of the indicators is labeled the dominant cycle. (second one down - brown).
The concept the underlies the minor cycle / dominant cycle relationships that have been touched upon is the Summation Principle. If you want to play around with its application you can download this teaching tool made available by Alex McEachern, the founder of Power Standards Labs. https://www.powerstandards.com/resources/teaching-toy/ The one you'll want to play with is the Harmonics Primer. When I discovered this 'toy' a decade or so ago I had several conversations with Alex concerning wave theory. One of the comments he made which shaped my understanding of stock market cycle analysis is that when Fourier Analysis is applied to any numerical time series it will always find cycles. This does not mean that cyclicality is in fact present in the numerical time series. Or to express it differently, it does not mean that the cycles found have any useful application when it comes to trading. In my trading, which for 30 + years has been driven by the concepts put forward by J.M. Hurst, the only cyclicality that matters is that which you can see. Years past before the advent of HFT, cyclicality and dominant / minor cycle behavior was clearly present down to a 5 min duration. These days I have to focus on 3 hr and 6 hr time periods to find consistent behavior. Without this consistency, which Hurst calls persistance, you do not have predictability and a basis to have an expectation of a highly probably outcome.
With cyclic analysis it is tempting to become attached to time. It is more important to learn how to recognize the changes in price behavior that are consistent with the cycle turns you are expecting. It is this change in behavior that tends to occur at (some what) regular intervals that is the cycle. A simple example of this can be seen on a 60 min candlestick chart with a 24Hr time frame. Notice the pattern of higher lows/highs changing to a pattern of lower lows/highs. If you count the bars between the swing highs and the swing lows you will generally come up with an average of 6 bars. Six hrs.... the approximate session of a 24Hr market. If you can find your way into that hrly candle that is making that swing high or low and you have a reasonable expectation that you are in the time and place in which 6 hr cycle highs/ lows are typically made then you have a reason to make a trade. In the NQ, these swings are generally good for 50 points.