Old Dog's Taming of the Beast?

The screenshot shows only a short period, could you please post a longer period (a whole year maybe)?

this can end without a warning! Be careful!

7bit are you using the arbomat demo ea from your thread or something different?

Its a slightly more advanced version that I will post soon. There is still one little bug in it that I want to fix before I post it.

Hello all,

Time to heed 7bit's warning on the basket!!

After behaving nicely for a year, the kernel is starting to wander out of whack as the GU and UCAD lose mirror symmetry. While it is still possible to find a nice regression, the cointegration statistics suggest a loss of stationarity.

Please don't trade this basket as of now until we see how things settle down.

I don't want anyone without the necessary experience to lose money!!

Best regards,

Old Dog

Hello all,

OK, the good news is that I have got to the bottom of the problem. After many hours of pouring over my old textbooks and many Matlab worksheets later, I know what the problem is!

We are forming these baskets by linear regression of a set of currency pairs, either onto a straight line (in the case of the Trend-O-Mat etc) or onto another pair.

The problem is multi-colinearity.

The problem we have here is one of spurious regression when there are linear relationships among the regressors. As is well known, currency pairs are correlated [Note 1] (and there are a number of websites dedicated to calculating these correlations hourly, daily etc). If the data is correlated, then the regression can be suspect.

This is what is happening here. It is trivial to compute a basket and the associated weights. The basket will "look nice" when plotted. But it harbours a dangerous secret in its heart!!

In order to be safely tradable, the basket must also be cointegrated (so it is stationary) as I have already explained at some length.

If we have multicolinearity, we cannot believe the statistics as we have a "rubbish in, rubbish out" situation.

The way to solve this is only to construct baskets from pairs with low correlations. So for example, EU and GU are too close to have in the same basket. Likewise, EU and UC are too close (but negative).

I have now constructed several baskets from pairs with very low correlations (<0.3) and have worked around the problem.

BE CAREFUL!!

Very best regards,

Old Dog



[1] You already know my views on "correlation" of non-staionary data!

I'm not a statistician (or how Cpt. Picard will say in 350 years: "I'm just an enthusiastic amateur")

I have just read the "granger 1974" paper (and understood ~10% of it ;-) where he talks about these spurious regressions and one thing that he demonstrates in this paper is that if you try to regress one random walk onto another one (the absolute levels) you will get "significant" coefficients almost all of the time (and the t-statistic seems completely meaningless) and the more independent random walks you include the worse it gets BUT if you instead regress the first differences instead of the absolute prices then the situation becomes much better!

This is also what I have observed while spending hours with moving my "now"- and "back"-lines around on the charts and watching the coefficients and the residuals plots changing its shape.

I have therefore included the option to do the regression on the price differences and it seems (in arb-o-mat, not in trend-o-mat) that the coefficients become much more stable but it also won't be able to (forcefully) fit every random nonsense any longer. This is more or less consistent with what I would have intuitively expected.

But as far as forex is concerned I do not believe that a regression on absolute prices is complete nonsense per se, they might look like random walks and they might be non-stationary but they might very well have enough in common that not only the differences but also their absolute values are indeed related. The only thing that might always be nonsense would be to allow a constant term (the intercept).

For example

XAUUSD = b * XAGUSD

makes perfect sense to me (although we are using absolute values) but something like

XAUUSD = b * XAGUSD + c

would be more likely to be a nonsense regression because I cannot think of any reasonable model that would justify the constant c in this equation.

The first order price differences are called "returns" in literature.

What I've also seen done is using logarithm of mid-prices to compute the returns instead of absolute prices - ln((bid+ask)/2), because 100 pips from 0.7 to 0.8 is not the same percent wise as 100 pips from 1.5 to 1.6. The logarithm solves this problem.

Hoho!

A quite understandable, and wonderfully optimistic thought!

Sadly, the facts say otherwise.

Guys, if you wish to follow this line, please remember that you are trading for entertainment, not profit. There is nothing wrong with that, of course, so long as you are are firmly aware what you are doing.

Old Dog

Only if you demand from the model that it must be 100% correct and will not create any losses. Only then the facts will most likely tell you that your model was wrong.

The same could be said about channels, trend lines, or whatever other strategy there exists.

If you allow losses (and have a defined risk reward ratio) and accept like in any other trading strategy too that these losses will happen then I don't see why it should be more dangerous than trading for example an ordinary triangle break on EURUSD or whatever else. The calculations of the needed lot sizes and stops and targets might be a bit be more complicated to correctly arrive at a certain risk/reward but otherwise it is also just another trading strategy.

If only 2 out of 3 regressions will give me at least one profitable trade before they prove to be "wrong" then it is already ok.

If I draw a channel into a daily chart and I successfully trade one or two more bounces from the channel boundaries and then a few weeks later it will finally break out of this channel and my third attempt to trade a bounce hits the stop, does this mean the whole channel was somehow "wrong"? Does this mean the whole concept of channels or ranges is wrong, only because they usually do not last forever?

It is more than just a thought and it does not only come from pure optimism:

If I do a regression on the returns (the first difference) and observe very constant and significant betas, no matter at which time I measure them then I believe I have a valid reason to assume that also the two original time series (the integrated returns) are at least not completely independent from each other. Then a linear regression on the absolute prices might very well give a more meaningful or useful result than pure nonsense or coincidence (the regression does not prove the model but IF there should really be some truth in this linear model then the coefficients will indeed have a meaning). This is essentially where my optimism comes from.

Hello all,

OK, let's confine ourselves to the facts here - I have found it helpful when dealing with mathematical strategies that "look nice" but may not be as useful when tested in anger...

I would refer readers to the standard text "Introduction to Linear Regression Analysis" by Montgomery and Peck.

On page 318 they give the definitive test for quality of a regression.

The steps are simple so readers can check this for themselves:

(1) Take the data matrix X. I have attached for your edification a 600 x 6 matrix of the daily closing prices of the AUDUSD, EURUSD, GBPUSD, NZDUSD, USDCAD and USDCHF for 600 days from 16/12/2008 thru 19/11/2010.

(2) Form the covariance matrix S = X'X, where ' is the matrix transpose operator. Obviously in this case you get a 6 x 6 matrix.

(3) Compute the eigenvalues of S and compute the ratio of the largest to the smallest.

That's it. It takes 30 seconds or less in Matlab, Mathcad or any similar math package.

Montgomery & Peck state that if the ratio is less then 100, you probably have a good regression you can trust.

If the ratio is between 100 and 1000, you have strong multicolinearity and the regression is suspect.

If it is over 1000, fuuurged-about-it. You have a totally spurious regression that is utterly meaningless.

You will note that for this basket of 6 pairs, the ratio is around 66,000.

So the regression is total garbage.

If, however, you take pairs with low correlations, this won't happen. I leave that as an exercise for the reader.

Very best regards,

Old Dog

Is there an easy explanation what the ratio of these eigenvalues actually means? Can you somehow illustrate or visualize *what* is actually measured by these eigenvalues and their ratios (other than that a regression would be spurious (and how so))?

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Edit: It seems you are trying to measure the amount of multicollinearity. But multicollinearity does not cause spurious regressions, this is an entirely different thing! Multicollinearity can lead to stronger fluctuation of some of the coefficients but this is not a problem for us and it is generally not a problem for the predictive power of a regression model!

It makes more sense IMHO to expand away from the equilibrium basket, say EJ=EU*UJ => EJ~EU*(1+d)*UJ (with |d|<<1) so that one can get a better control over the basket's movement, since it is not established by a fit.

k