Adaptive System vs. Curve Fit

I was developing a day trading system that looked at criteria for breath indicators (non-price based).

The system did well but traded against the trend often. Since I was using hour bars, I added a moving average trend filter that said only trade in the direction of the trend. I used a length of 70 (for 10 days total).

I optimized the length parameter testing range 35 to 105 increment 7. All the settings were profitable, so this validated I had a quality filter ... it just so happened that 63 (9 days) was the most profitable, but I left it at 10.
 
Originally posted by TriPack
Let's say the old value was 150, and the optimized value is 275 (in the optimization I use minimum increments of 25). I would then add 25 to the next day's value, so tomorrow I would use 175 as my Length.
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what you are implicitly assuming is that the optimum value, as a function of time, has a strong low-frequency "signal" component and high frequency "noise" component. by limiting the daily change of the parameter, you are effectively applying a low-pass filter.

whether your parameter satisfies that assumption is actually trivial to test. just construct the following historic series:

a) historical optimal values
b) historical optimal values, shifted by one day to future
c) approximated optimal values generated using your method

and then calculate correlations CORREL(a,b) and CORREL(a,c). if CORREL(a,c) is noticeably greater than CORREL(a,b), then your method is justified.

- jaan

p.s. another thing that you are assuming is that similar values of the parameter give, on average, similar profits. that may not necessarily be the case.
 
I think that your idea is sound but the approach is suboptimal.

If you want to have an adaptive component, I'd recommend you pick a way to change the paramater that is not a direct function of the "optimized profitability" for the system. For instance, if you have a "length" or periodicity in a moving average or such, I'd recommend that you vary it with the dominating period at the time. Another choice might be to find the parameter value that produces the best signal to noise ratio at the moment.

If you include system profit in your optimization of the parameter directly, you're really just finding the fixed value that historically would have worked the best, not the value that at the moment is optimal (by some metric)
 
Originally posted by vikana
I think that your idea is sound but the approach is suboptimal.

If you want to have an adaptive component, I'd recommend you pick a way to change the paramater that is not a direct function of the "optimized profitability" for the system. For instance, if you have a "length" or periodicity in a moving average or such, I'd recommend that you vary it with the dominating period at the time. Another choice might be to find the parameter value that produces the best signal to noise ratio at the moment.

If you include system profit in your optimization of the parameter directly, you're really just finding the fixed value that historically would have worked the best, not the value that at the moment is optimal (by some metric)
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Thanks for your comments. I'm a bit confused. How would I go about figuring out the dominant period of the time of the indicator (in this case a smoothed RSI)? How would I find the best signal to noise ratio at the moment?

I originally thought maybe just using the length that optimized with the highest net profit might prove best for the next day. The problem was that it jumped around too much, and wasn't much better than just using a single value over all days.

The goal of this optimization routine is to find the value that will increase the overall consistency of the system and produce the best profit for the next day. Any additional tips would be appreciated.
 
Originally posted by TriPack


Thanks for your comments. I'm a bit confused. How would I go about figuring out the dominant period of the time of the indicator (in this case a smoothed RSI)? How would I find the best signal to noise ratio at the moment?
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this is unfortunately complicated to answer. The engineering discipline is called "signal processing" and contains lots of good research on how to calculate spectrums, dominating frequencies and so on. Almost all the material is mathematical in nature, so depending on your background it's either difficult or not.

There is one good recent book by John Ehlers called Rocket Science for Traders (or something like that). Ehlers offers a somewhat simplistic approach to determining the dominating frequency (under a certain set of assumptions). It works surprisingly well, given how simple the approach is.

Signal to noise is also fundamentally a signal processing concept and can be found in the same literature.

I hope this was of help. I can probably dig out a few signal processing references, if that would be of interest. I suspect that a search on Amazon will give you more hits than you can read in a lifetime :)
 
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