Synthetic hedges, cointegration, mean reversion and similar stuff

Hello, MB

Could I just take this opportunity to thank you very much for posting this link to the OU paper. Finally over Christmas I have had chance to sit down quietly and read it. It has been a long time since I read such an interesting paper. So many pennies dropped reading this!! Several sets of scales have fallen from my tired old eyes!

If you look at the "standard" econometrics literature (where no-one has a clue about linear algebra), they bang on at huge length about the differences between MA and AR processes, how to combine them into ARMA, endless tests for distinguishing trend-stationary from difference-stationary series, endless variations on the Augmented Dickey Fuller tests where you can get any answer you want by fiddling with the parameters! Blah blah blah ad nauseam!

The OU framework presented in the article is brilliant. It is so straightforward once it is laid out in simple terms. Once you have projected the data into the eigenspace of its own covariance, everything else follows from standard control theory and state-space analysis that any engineer will be familiar with. We are on safe and familiar ground at last!

We can now dispense with all the various unit root tests etc etc and distinguish exactly what sort of animal we are dealing with simply from the partitioning of the eigenspace. We can separate the stationary and co-integrated parts (and note carefully from the paper that these are NOT interchangable!) from the non-stationary parts. We should now be able to build baskets with rigorously provable finite variance and a significant chance of profitability with quantified risk control.

Very nice indeed. Thanks once again for your valuable contribution. Posts like that one make FF the diamond mine it sometimes is. OK, you have to shovel through tons and tons of crap, but now and again you find a real sparkler!

Very best regards,

Old Dog

And then, tnx for your review. There should be more reviews of good articles on FF so one can make better use of his time.

It's good to see people posting interesting stuff like this paper, proof that intelligent life does lurk on FF. I've also been looking at PCA approaches to stat arb.

I tried running both EAs on the same chart and here's what I've got:

I don't quite get the difference in the moves even though they follow the same pattern.

try setting the arbomat to diff=false and/or try longer timeframes

Comparison of all Recycle methods

I have tried to do a quick and dirty replacement of the simple least squares fit by principal components regression, using the pcr() function from R's "pls" package. However, the coefficients are fluctuating wildly using this method, don't know why, so far. I have not yet tried different settings, e.g., how many components to use in the prediction.

Partial least squares regression (plsr() in the same package) yields good results. Have so far not done extensive comparisons to the results with lm(), though.

From Wikipedia: "PLS is used to find the fundamental relations between two matrices (X and Y), i.e. a latent variable approach to modeling the covariance structures in these two spaces. A PLS model will try to find the multidimensional direction in the X space that explains the maximum multidimensional variance direction in the Y space. PLS-regression is particularly suited when the matrix of predictors has more variables than observations, and when there is multicollinearity among X values. By contrast, standard regression will fail in these cases."

To use PLS regression with Arbomat and Trendomat, do the following:

1. At your R prompt, do install.packages("pls")

2. In the EAs, replace
Rx("model <- lm(y ~ x)");
by
Rx("model <- plsr(y ~ x)");

Rx("model <- lm(y ~ x + 0)");
by
Rx("model <- plsr(y ~ x + 0)");

Rx("pred <- as.vector(predict(model, newdata=data.frame(x=I(regressors))))");
by
Rx("pred <- as.vector(predict(model, newdata=data.frame(x=I(regressors)), comps=1))"); //using only the 1st component

3. Put Rx("library(pls)"); at the beginning of the onOpen() function (have tried to place it in init(), but this didn't work (why?)).

This is strange. It should work in init() and this would be the natural place to put it. Is there anything in the debug output (debugview.exe) that might explain what goes wrong?

(I will try your modifications too next week)

Hey 7bit!

First, thanks for the trend EA, it is great. I've had succesful trades on the 30M, H1 and D1 charts! On D1, it is extremely profitable though a bit longer to get rolling.

By the way, if you're still using it, when do you buy/sell a basket? The only entry signal I use is that the basket has to be outside of the 2 st dev lines.

If anyone is interested, I can post the entry and exit charts of my trades.

Thanks again!

I couldn't find anything useful in the Debugview output. It shows "Error: could not find function "plsr" " just as if the pls library hadn't been loaded.

In my first post I forgot that in the EAs you also have to replace every occurence of

coef(model)
by
model$coefficients[,,1]

Here, [,,1] again means that only the first component is used,, [,,2] would correspond to the first two components being used, etc. Don't forget to also change predict(..., ncomp=1)) accordingly if you want to play around with the number of components.

The more components are used, the closer the plsr() model will approach the lm() model. Some interesting results:

(USDJPY coefficient scaled by 0.01 in the ncomp=1 graph, by 100 in the others)

And two more with longer back_bars over a longer period. USDJPY coefficient again scaled by 100.

Hello Ultfrisbee, few charts can't hurt. I would like to see those.
Thanks.

I have just gotten up to speed on this and am anxious for this thread to keep chugging alone. Did I miss something?

KingHigh

As I stated in the previous post, I am very interested in this statistical approach to trading baskets. I have been working on basket strategies for a while and have been baffled by how baskets tend to perform - many times contradictory to what I would expect.

So - I am going to take one of my synthetic candle indicators and convert it to build basket candles based on the coefs generated by 7Bits EA for the targeted basket pairs.

At this point, I am not able to draw any real conclusions on how the baskets are performing, so maybe this will be a good first step for me to solve this problem.

If this all pans out, maybe I will create an offline chart generator for custom baskets with their calculated coefs ( ala RenkoLiveCharts ).

KingHigh

As I post yesterday, I wanted a tool to look at the basket results to see how they correlate with the Arb-O-Mat spread curve.

This is just a prototype showing the basket bars. In the Arbomat, I show the 1 an 2 deviation levels against the spread line - Pink, Red, LightGreen, and Lime objects.

Next, I am going to convert the ArbOMat to an Indicator so that I can do some backtesting where I can put the ArbOMat on top of the basket bars to get a better perspective.

If there is anyone else out there - stay tuned.

I am also anxious to see if the primary componet stuff pans out.

KingHigh

Recycle2 - Tools for Statistical arbitrage

This won't be easy. Its doing long-running tasks that are not allowed in an indicator, it will freeze and block the GUI and be no fun to use. You should instead try to include your trading (or backtesting) code into arbomat itself and call it at the end of start()

7bit,

Yes in deed, the indie will freeze up the GUI, but I don't care. I am using the indie as a visual test tool to see the historical relationship of the spread moves as a function of std dev, to the consolidated P&L of the basket of currencies weighted by the calculated coefs as lot sizes. In no way is this a practical tool for real time use.

Making good progress, but have some problems - probably because of my lack of knowledge about R.

KingHigh