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Cycle measurement: the easy way

  • #41
  • Jul 21, 2014 10:08am Jul 21, 2014 10:08am
Quoting Trainman
When you say "lag", do you mean phase shift?
By "lag" I mean what any trader in the forum understands: the delay in samples (bars) between the input and the output. For instance a SMA20 lags 10 bars. I consider the worse group delay in the band pass because the phase response isn't linear.

Quote
In your first post you mentioned that your goal was to null out the cycle and be left with the trend. So when you say a lag of 4 bars is too much, it sounds like you are talking about a systematic phase shift. If the approach is to generate a sinewave equivalent to the cycle and subtract it from the data, that can readily be done without any phase shift. But you would have to wait for enough of the wave to appear to be sure it was a cycle. Additionally, your period estimate would have to be extremely accurate, or the inaccuracy of the period will...
Substracting the main cycle from the data is indeed the idea of the approach. I don't have an extremely acurate estimation of the period. This is the major problem. As you can see in the post #4 the phase is absolutely not linear and the delay curve raises sharply in the frequency band of interest. Because of this very big slope a small error in the estimation of the frequency leads to a huge error in the determination of the lag. For this reason I cannot compensate the lag by advancing/backsteping the sinewave by the lag. This is why I try to have a very low lag so the error is kept small.

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I use a lag-free LPF to detrend data as a preparatory step to cycle detection. But data points at the far right edge of the chart are necessarily only approximations. In my work, the error this introduces is insignificant. The cycles extracted in this way are free of phase shift. But you are not going to see instant results, it takes a few turns of the cycle at least to get reasonable estimates of period, amplitude and phase.
Goertzel filter gives similar results but I need the frequency+phase+amplitude almost realtime because the cycles are so short lived. Goertzel filter needs 3 periods of the cycle in theory but only 2 can already give a good result. Unfortunately some cycles just don't last more than half their period. If I substract a cycle that is already gone I actually introduce a fake one.

Quote
Another point is that the SNR of market data is low at the best of times. If your method cannot stand up to 4 bars of lag, it sounds like it would also be overly sensitive to noise in the data.
No as I said the low lag is only required for the acuracy. The output is due to be fed into a kalman filter. The issue I have is that the cycles which are at the limit of the trend wavelength make the KF oscillates (post #1) because it cannot decide if it is a trend or a range. Short and very long cycles are no problem. If I was interested in cycles of periods of 10 bars and less the method would work perfectly. But I target cycles of 10 to 25 bars.

If 8 bars of lag is acceptable for you wavelets are a good and fast solution.
No greed. No fear. Just maths.
  • #42
  • Jul 21, 2014 2:30pm Jul 21, 2014 2:30pm
Ah! The picture comes into clearer focus. I don't have anything else to suggest, ATM. It is unfortunate that market data is not better behaved.

A cycle to one trader isn't a cycle to another. In my world, a cycle isn't a cycle until it clearly projects forward in time. I use three rotations to obtain initial measurements, and then I watch and wait. If price data continues to follow the trajectory plotted forward in time for that wave, then that's a cycle. If it doesn't then it never was a cycle, but only a noise burst at a particular frequency. What I'm looking for are cycles that have long lifetimes, they persist for 8, 12, 20 or more rotations. Most "cycles" in price data are just short-lived bursts, and I don't know of any automated way to screen them, it remains a manually intensive process.

My present research direction is in frequency adaptive BPFs. I want to take a spectrum of the price data, extract the dominant cycle and then tune a BPF to that. Raw price data is far too noisy for a Hilbert Transform to obtain a stable frequency estimate directly. Researching the subject brought me to this thread. You have an interesting approach to cycle measurement, a bank of BPFs of this type might do the trick. BPFs might not track a cycle well if its period strayed far, so another approach that I'm considering is Empirical Mode Decomposition. Do an EMD, then pick out the IMF of greatest interest (highest amplitude, generally) and HT that for the instantaneous frequency. It should be stable enough for my needs, though I don't have any experience with EMD to know how much edge effects will get in the way. This seems like the most promising approach for now.

I haven't looked into wavelets at all.
Sure I have a trading plan. Buy low. Sell high. What's yours?
  • #43
  • Jul 21, 2014 4:20pm Jul 21, 2014 4:20pm
What periods range do you focus on?
No greed. No fear. Just maths.
  • #44
  • Jul 21, 2014 5:43pm Jul 21, 2014 5:43pm
Quoting PipMeUp
What periods range do you focus on?
I'll look at a wide range. After all, a trend in one TF is a cycle in another, and what is noise at one TF will often display structure at a lower TF. But the periods I work with most are in the range of a few hours to a few days. You need to watch the activity on three or four TFs though. Anyone that has traded cycles for an appreciable time knows that trends tend to play havoc with cycle trading. Too many times I've been blind-sided by something I didn't see coming, but a postmortem review revealed that the signs were plain on higher TFs if I'd been watching for it.

Were you expecting an answer in number of bars? I count my cycles in units other than bars, e.g. hours, so I can easily flip TFs and see the same cycle at different levels of detail without having to re-enter parameters. So number of bars varies, but 50 or 100 would be typical.
Sure I have a trading plan. Buy low. Sell high. What's yours?
  • #45
  • Nov 30, 2015 2:39pm Nov 30, 2015 2:39pm
During years, I have tried to measure cycles like you, but finally with two moving averages and a good osciltor you can get very good results without high level of maths and DSP.
Attached Image (click to enlarge)
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  • #46
  • Dec 1, 2015 6:05am Dec 1, 2015 6:05am
As I explained and unlike what the screenshot suggests the goal is not to pick entries. It is to reduce the residual oscillations of a trend measurement.

What is the "good oscillator" you use? Based on which criteria do you consider it good?
No greed. No fear. Just maths.
  • #47
  • Edited Dec 4, 2015 1:15am Dec 3, 2015 9:25am | Edited Dec 4, 2015 1:15am
I use MACD like a oscillator.... Its good because gives me the best turning points.

Maybe I cant help you because you are looking for good estimator of the trend and I prefer the best entries.

Whats the trend ???

Do you have investigated the distance beetween two dominant cycles ??

For me it is impossible to extract the perfect cycle, only an approximation..
  • #48
  • Dec 3, 2015 9:51am Dec 3, 2015 9:51am
Your answer is quite surprising because mathematically MACD is an estimator of the trend...
No greed. No fear. Just maths.
  • #49
  • Dec 3, 2015 1:41pm Dec 3, 2015 1:41pm
It depends like you use...
  • #50
  • Jul 22, 2024 3:14pm Jul 22, 2024 3:14pm
Hi,

I am looking for John's Mesa Algorithm. to compute the dominant cycle
- is it in MESA and Trading Market Cycles (2nd Ed)?

Most sources i have read point to the Homodyne discriminator or AutoCorrelation periodogram
  • #51
  • Last Post: Jul 22, 2024 3:24pm Jul 22, 2024 3:24pm
Quoting PipMeUp
Sometimes when you search something you find something else... I was (and still am) looking for a good estimator of the trend. Without being a DSP guru, whoever played around with some moving averages quickly realized that if you want the result smooth you get lag. You can remove the lag but you get overshooting; which is as bad. To reduce the overshooting you give back the smoothness. A vicious cycle with no escape. I'm no exception and my trend estimator suffers from annoying residual oscillations. Those oscillations are mainly due to the wide...
Is it a kind of pattern recognition algorithm or smth?
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