I would like to introduce you my findings in the mathematical approach to cycles.
But before that, I would also like to tell you that all my work is inspired in William Randall’s fantastic contribution to cyclic analysis with his Hurst band-pass filters. Since I saw for the first time one of his graphs I felt hooked by it. I would like to publically thank William for all his help and teachings. But also to deeply thank David, for developing ST and for the superb educational effort he does every day. I still think that the final job to do in the near future is to merge, as much as possible, both approaches.
I also want to thank A.S. for putting all his programming skills in this task.
Since I understood William’s techniques I tried to replicate them but I also tried to do something different in order to contribute with something new and interesting…. although I must say that I don’t have clear if the approach I do is different neither interesting
The fundamental basis of my approach is to find out which is the current best oscillation that best fits with the current market action. Probably, the Principle of Variation is the most unclear principle for me. We may all agree that cycles varies in wavelengths and amplitudes but we may also agree that the way they vary is absolutely a mystery, at least for me. Hurst said that this variation is smooth along time but we have a lot of examples that sometimes they do sharply, sometimes we find very stable markets, with a clear wave for many time but other times not. I think it is true that there are solid nominal cycles but I feel we must be more flexible in how they relate each other (I would agree with William about quite complex harmonic relations that mutes over time) and the variations they suffer.
I think it is better to show you some graphs in order to see how the analysis works. I’m going to show you 3 graphs about the SP500, a 8h chart, a daily chart and a weekly chart.
SP500 8 hour chart
In the 8h chart the current best oscillation is the shown bellow, it would indicate that a nominal 40 day cycle is dominant in this time frame.
SP500 Daily chart
In this case, the dominant cycle is the 80 day nominal cycle running a bit longer than before, the harmonic is a perfect 2:1 to the 8 hours’ 40 day cycle
SP500 Weekly chart
In this case I show two waves, the corresponding to a 18 months nominal cycle and the 4’5 years nominal cycle. I want to explain a particular situation when using this technique; you can observe in the upper oscillation, the 18 month wave, a flat behavior for some time (market with an arrow), this happen when the price do a subtle trough, when it happens I understand that the market is “straddling” that cycle, as it seems to be happening.
Taking into account this aspect, the harmonic behavior, in this case, is perfectly Hurst in all graphs, in this last one, with a relation 3:1.
Apart from showing this approach, we can see the special junction where the market is. It is not a question of opinions, you can extract your owns by observing these graphs.
Hope this help!