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Attachments: Nonparametric Association Measures in Systematic Trading
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Nonparametric Association Measures in Systematic Trading

Quoting staassis
{quote} Ok, great, but how did the strategy perform over the whole of [Jan 25 European session + Jan 25 US session], with EUR/USD going from 1.24 to 1.253 and back to 1.237. I would imagine the strategy to perform better in calmer waters.
correct; it does perform better in calmier time. Perhaps one should add some filters to exlcude high volatile times.

The approach that I take with this strategy to increase profitability and reduce risk; is to play the law of large numbers. we must diversify the strategy across multiple settings (timeframe, period, moving average type, entry and exit deviation thresholds, etc), and multiple instruments.

this way you can manage a portfolio of positions open at any given time; and the risks will cancel each other out.

here are 3 trades during NY session; one winner, one loser, and one breakeven
Attached Image (click to enlarge)
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here is a live trade right now open for USDJPY

two prior trades were closed recently; as you see from the green arrows
Attached Image (click to enlarge)
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Quoting PipMeUp
If you do this and keep considering it as a spread it is like you force the weight of the second asset (the MA) to be 0. The asset price becomes a "rough approximation" of the spread which can become very far "off target". Are you going to correct it by continuously "re-balancing", that is adding more and more to a losing position? Look on the chart you posted above I can see at least 8 big losers. I doubt the tiny winners will balance.
PipMeUp, i came across this blog which talks about the same strategy above.

https://forums.babypips.com/t/statis...egy/42993/1308
Quoting alphadude
{quote} PipMeUp, i came across this blog which talks about the same strategy above. https://forums.babypips.com/t/statis...egy/42993/1308
His maths are wrong. He starts from a wrong equation then he takes (correct) deductions starting from his mistake...

Let's start with the proper equation y=βx+σ²ε <- he overlooked the uncertainty (aka noise) σ²ε !!
The assumptions are that
- The expectancy of the noise E[σ²ε]=0 because it is the model assumption of a linear regression.
- The variance of the noise V[σ²ε]=σ² because a linear regression implicitely assumes white noise.
- It is supposed to stay like that. It is not actually the case that's why there is a need to rebalance.
We can rewrite it the usual way: y - βx = σ²ε. This implies you buy one unit of E/U and sell β units of G/U when the noise part (aka misprice) is far away from zero. This "far away" is a function of the variance.
What is traded is neither EUR/USD nor GBP/USD. It is not even EUR/GBP. It is the noise σ²ε. The goal is to fade the noise under the assumption that it is expected zero reverting because one of the pairs is "mispriced" according to the other for some fundamental reasons.

But let's rewrite the equation his way: y=βx+σ²ε => β=(y-σ²ε)/x.
Setting x=EUR/USD and y=GBP/USD you get (EUR/USD - σ²ε) / GBP/USD ≠ EUR/GBP <= It is not EUR/GBP and it can (and will) be very different.
When you go long E/U and short G/U one should compensate the loss of the other when they start trending. At least if the fundamental relationship actually exists. At mean reversion the positions are in profit. When you only open a position on E/G nothing compensates the loss when it starts trending in the opposite direction. At mean reversion the position will be in loss. When it starts trending in the direction of the position the position is quickly closed at the MA cross.

Please don't misunderstand me. I'm not rejecting your idea in bulk. It is simply not stat-arb. That's it. I see a very high risk associated to limiting the profit with big potential loss. I disagree on the mean reversion because data show so: https://www.forexfactory.com/showthr...10#post8466810

Actually I thought about some way to "trade the MA". I realized that if the MA is a proxy for the price the price is a proxy for the MA too. I couldn't find any time to work on it. Roughly the idea is to buy proportional to the price is below the MA and sell or buy proportionally to the slope of the MA. The net value gives the size of the position to open. You can continuously "rebalance". The good thing is that when price trends your position is in the direction of the movement. When the market ranges the MA is either flat and it becomes equivalent to your method or the MA is like the price with lag. This is where the loss is big. But so is your method in this regime.
No greed. No fear. Just maths.
Quoting PipMeUp
{quote} His maths are wrong. He starts from a wrong equation then he takes (correct) deductions starting from his mistake... Let's start with the proper equation y=βx+σ²ε <- he overlooked the uncertainty (aka noise) σ²ε !! The assumptions are that - The expectancy of the noise E[σ²ε]=0 because it is the model assumption of a linear regression. - The variance of the noise V[σ²ε]=σ² because a linear regression implicitely assumes white noise. - It is supposed to stay like that. It is not actually the...

interesting journey onto the stats arb in forex. I have read some posts in your pairs trading threads; and it rings bells all the way. Been there; done that; and I understand your frustrations. After a while I have concluded that simplicity wins.

Say for example that you have found 2 cointegrated instruments; the white noise is gaussian; and the relationship was stable historically. There is no guarantee it will remain so. how do you trade it? presumebly you will define some deviation threshold and fade the moves.

After a while; that cointegration relationship will break temporarily or forever. How do you detect that so you can avoid the losses?

the answer to that will be to use a standard deviations (aka bollinger bands). That will not work either; unless you use a moving standard deviation; and et voila you end up using a moving average.

since a moving average is used by many to solve the mean drift issue of the spread; why not use it for non-cointegrated pairs then. Basically throw away all those cointegrated tests; and stick to the solution that solved the mean drift issue.

the moving average is indeed a powerful tool that solves a very difficult problem in statistics. There are quite a variation of moving averages; including Kalman filter; to which they all attempt to solve the same problem.

My favourate read on this subject; is that chapter 2 by James Altrucher. Although he is not a hedgy; but he did hit the nail in the head when he described the unilateral pairs trading strategy in his book.
Quote
Say for example that you have found 2 cointegrated instruments; the white noise is gaussian; and the relationship was stable historically. There is no guarantee it will remain so. After a while; that cointegration relationship will break temporarily or forever. How do you detect that so you can avoid the losses?
Did you read the part between 7bit and Old_Dog? In short Old_Dog's position was that you shall compute the cointegration and statistically validate it is still present. Either you rebalance the basket or you stop trading because it is no longer a basket. The problem is that the statistic tests (ADF and al.) are weak, very weak. 7bit's point of view was that the tests are so weak that in general they cannot discriminate. His solution was simply to pretent the assets are cointegrated while keeping in mind they perhaps are not at all. Then you rebalance more often. => He piece-wise linearizes the problem.

Personnally I never found co-integration between any pair of FX pairs. In the European indexes I found something between CAC and DAX and between CAC and IBER. Strangely nothing between DAX and IBER (no transitivity).

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how do you trade it? presumebly you will define some deviation threshold and fade the moves.
That the point of the link to my post. You can't do that because the relationship is not linear. You can fade the deviation when it is small. But you follow the deviation when it is big. The problem this creates is that if you need be (say) long at -1sd but short at -3sd you have to be flat in-between. But this can only happen if you were long and price went against you: you are in loss. Additionally I think it is more complex than that. I suspect that both the deviation and its rate (direction toward or away from the mean) have to be taken into account. Also the effet of the trend has to be taken into account (the picture is for flat trend) because it will distort the estimate of the deviation due to the combined effects of the lag and the non-linearity of the filter (MA).

Quote
the answer to that will be to use a standard deviations (aka bollinger bands).
I agree this will in the end be equivalent to a rolling Z-score. I strongly warn you against the use of Bollinger bands. The non-normality of price returns is not the main issue: https://www.forexfactory.com/showthr...55#post7676955

Quote
Basically throw away all those cointegrated tests; and stick to the solution that solved the mean drift issue.
No problem with that. I just refuse to consider a problem is solved by pretending the problem doesn't exist.
No greed. No fear. Just maths.
like Ed Sakota says; everybody get what they want from the market
Quoting PipMeUp
{quote} I remember a post by the redlion (I can't find it) where he showed an up trend containing more down bars than up bars. The trend was created by a minority of big up moves.
That's a very good observation.The big question is how to differentiate the trend?I am not convinced by hurst exponent or maybe I am stupid.
Quoting herbie88
{quote} That's a very good observation.The big question is how to differentiate the trend?I am not convinced by hurst exponent or maybe I am stupid.
the definition of trend depends on your trading idea; anybody can define a trend; and trade it.

it also depends on the timeframe you are looking at.

best is to observe the market (through screen time in live market or backtesting mode); come up with trading ideas to define the trend; and test those ideas. if they work; hell that's the trend.
I am rather looking for mathematical definition of the trend but my opinion is ,there is no perfect mathematical definition of the trend.
I am using the slope of the Holt - Winters double exponential forecasting indicator.

I check 2 things with different time frames; first to see how close the buy sell signals to peaks and valleys(higher high- lower lows) then check the amount of signals
including the false signals.Perfect scenario always fade away after some time ,therefore switching from timeframe to timeframe is necessary.But I need to put all this in a fully working automatic expert advisor.

In this website here http://www.financial-hacker.com/the-...eanness-index/ the author claims that his MMI indicator improves the trend following systems and it prevents false signals.I havent checked the MMI indicator to see if his claims are valid.

I have another filter in my mind that is instead of closing the signal at open or close ,predict something with machine learning.
Quoting herbie88
I am rather looking for mathematical definition of the trend but my opinion is ,there is no perfect mathematical definition of the trend. I am using the slope of the Holt - Winters double exponential forecasting indicator. I check 2 things with different time frames; first to see how close the buy sell signals to peaks and valleys(higher high- lower lows) then check the amount of signals including the false signals.Perfect scenario always fade away after some time ,therefore switching from timeframe to timeframe is necessary.But I need to put all...
if I were you I will stay clear from machine learning. it is a hype
I agree and I disagree with you.I disagree because I enjoy the benefits of machine learning (prediction,classification and clustering)
Check this excellent discussion ,what works and what does not work with ML:
https://www.elitetrader.com/et/threa...1#post-4356023
https://www.elitetrader.com/et/threa...5#post-4294233
https://www.elitetrader.com/et/threa...300585/page-11
Quoting herbie88
I agree and I disagree with you.I disagree because I enjoy the benefits of machine learning (prediction,classification and clustering) Check this excellent discussion ,what works and what does not work with ML: https://www.elitetrader.com/et/threa...1#post-4356023 https://www.elitetrader.com/et/threa...5#post-4294233 https://www.elitetrader.com/et/threa...300585/page-11

are you using ML successfuly?
I am using several softwares from Ward systems plus some R -mql4 interface (Hidden markow model) and yes they are succesful.But I havent' been able put them all in fully automatic manner.Ensemble methods always work better then the single ML algorithm.
Quoting herbie88
I agree and I disagree with you.I disagree because I enjoy the benefits of machine learning (prediction,classification and clustering) Check this excellent discussion ,what works and what does not work with ML: https://www.elitetrader.com/et/threa...1#post-4356023 https://www.elitetrader.com/et/threa...5#post-4294233 https://www.elitetrader.com/et/threa...300585/page-11
Dear Herbie88,

I have read the threads you have linked. Frankly, I do not know why you have referred to them because they are quite "light" (read "stupid"). The only advice they give is "use Python". They do not characterize Machine Learning positively but rather compromise it... I use machine learning regularly, but I would like to be believe that I do this in a more robust fashion. My gut feeling as well as substantial (but not extensive) experience says: do not trust neural networks. I use other methods instead. Those other methods lead to a strategy which I am illustrating in the graph below. I trade a modification of that strategy regularly (but not the exact version, and not always). I am mildly profitable. Want more, of course.

P.S. Were you really born in 1988? Hail to you.

.
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Quoting staassis
{quote} Dear Herbie88, I have read the threads you have linked. Frankly, I do not know why you have referred to them because they are quite "light" (read "stupid"). The only advice they give is "use Python". They do not characterize Machine Learning positively but rather compromise it... I use machine learning regularly, but I would like to be believe that I do this in a more robust fashion. My gut feeling as well as substantial (but not extensive) experience says: do not trust neural networks. I use other methods instead. Those other methods lead...
Hi Stass, in the above equity curve you uploaded; how many trades per year?
Quoting alphadude
{quote} Hi Stass, in the above equity curve you uploaded; how many trades per year?
Depends on the specification. In the graph shown above, the number of trades per year is approximately 244. Most of the time is spent in the idle state, as each trade takes only several minutes.... Not saying that this is the best way to trade AUD/CAD. Just illustrating the potential in machine learning.
  • Post #58
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  • Last Post: Edited 11:47pm Jan 15, 2021 11:37pm | Edited 11:47pm
Another reference on Spearman's rho in detecting change in dynamics of an asset. The formula-dense pages can be skipped on the first read... This paper is nothing terribly insightful but it may serve as yet another test / signal to implement in somebody's analytics.
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