Cointegration and mean-reversion

[crowlogic]

I didn't mean remove the autoregressive terms, only the constant terms. Othewise the forecasts would be biased to drift up or down over time instead of forecasting 0 return in the long run?



Thanks for the links on the books.. I'm ordering them now. I already have 'Applied Quantitative Methods for Trading and Investment', 'Likelihood-Based Inference in Cointegrated Vector Autoregressive Models' very heavy on the math but I am getting some useful stuff out of it, and several others 'Market Models', some books from Olsen, etc.



Re: multiple time frames.. I started running some experiments, estimated VECM models at my highest frequency, then reducing the frequency on the same data and re-estimating the model.. the cointegration vectors are very similiar and provides even better r-squared values at lower frequencies.. are there any methods to determine the optimal aggregation frequencies.. should high frequency predictions be fed into the lower frequency models, or should they only operate on input from the low frequency models themselves?

[dgn2]

Yes, that is what I would expect. The r-square values should be higher for lower frequencies because the correction term should operate at a lower frequency.

[crowlogic]

Makes perfect sense, should I be concerned if my some of my error-correcting terms are positive? Seems to imply some of the variables are moving away from equilibrium.

[crowlogic]

[i]crowlogic, I don't think you will find a single optimal forecast horizon. I would suggest looking at a set of horizons, particularly to start. I am also not sure that you want to remove the auto-regressive terms. I definitely wouldn't.[/i]



Ahh, spectral methods.. I don't know why I didn't think of this earlier, price series are composed of any number of a series semi-periodic waves, an appopriate set of filters can be designed (automatically with SSA) such that they carry the most of amount of power to the least amount.. The power at the different frequencies orbit arond some chaotic attractor in the short term.. and then use the cointegrated long run relations to help guide longer term forecasts.

[Omega]

I have a feeling I'll be shot for asking this question but I'll ask it anyway. Once you carry out Johansen test you get a reading of how many cointegrating relationshipps there are. But how do you decide which relationship to use?



e.g suppose you 10 stocks and what to see if there is a cointegrting relatioship. You carry out johansen methodology, gt that there are 5 cointegrating relationships....but then which one do i use??

[Baltazar]

heu maybe it should tell you you should try to find cointegration relationship between subaskets of your 10 stocks...



why?



well if you have a cointegrated pair, it will be more easy to trade then a combination of 10 stocks