Playing with Cycles (part 1?)

Some of you might remember back a few days ago, that I now had time to return to research since the book I was writing is 'at the printers'. Well, cycles are something I hadn't investigated much in the context of exponential time. My preliminary results are very interesting.

On studying the literature, I found that the usual procedure was to take the raw data, detrend it to make it less 'lumpy' and to take the 'tilt' out of it, whether up or down, then run a Fast Fourier Tranform on it to find the 'cycles'. I picked up the book 'Rocket Science for Traders' and saw the work done there. I came to the conclusion their methods were all flawed by the fact that if a particular cycle failed to show up in price action (as, say, a local low at that point),on a given date, it was lost to the software analysing it.

By looking at fast oscillators, like Williams %R for instance, I noticed that it was showing a lot of cycle activity that the other researchers were missing, because it didn't always translate into a big price move. With that in mind, I started picking cycle bottoms as calendar dates off of charts using Willaims%R and occasionally RSI, and then plotting them to see if I could figure out the cycle period.

I quickly realized on looking at the data, that sometime cycles of regular period were indeed showing up in the exponential time field, but sometimes the cycles were erratic, and not holding to a constant value (in terms of exponential node spans, not calendar days, of course). It was clear, however, that when plotted exponentially, the changes in Elliot Waves were made very apparent!

I am showing two charts here, of the same data. Using the Weekly chart of the $NDX, I picked off 18 values from the 10/8/02 bottom to the recent price action.

The bottom chart shows the cycle bottoms plotted against the average cycle time (all in normal calendar time), which, not surprisingly is an uninspiring and useless chart. This is what was produced first, as a control case. Then I created the top chart which shows the same dates plotted as node values against a chosen node cycle, and suddenly they group into linear segments defining the run time of individual Elliot Waves. I have labeled all of the cycle bottom dates used (the same dates plotted without labels in the boring, calendar time, lower chart) and also marked are important transitions. This has been done for two other bear market rallies (not shown) with the same results. Obviously, this has to be repeated many more times in backtesting, but I think I'm on to something here....