I’ve been thinking about the relationships amongst a network of assets. Supposing I have a network of hundreds of assets, what sort of measurements can be made that allow for statements about the future state with a measurable degree of confidence.

Here are some “standard” approaches to looking at the relationship between assets:

**Covariance**

Covariance is a linear measure, the normalization of which is literally the slope of a least-squares regression line through paired data. Has issues with lagged series and assumes linearity, also only uniquely specifies elliptical distributions.
**Cointegration**

Cointegration is a measure of relationship between series using an autoregressive error correction model. It avoids many of the issues of Covariance, however, like covariance is not sufficient to uniquely specify the joint distribution. The VECM model and Johansen method give robust estimates of this.

**Distribution Estimating Models**

Models that estimate the distribution (i.e. provide the most probable price movement in the next sample period based on an estimated high-dimensional distribution); works well on certain portfolios.
**SDEs**

SDEs that impose a structure / mechanism of price movement, implying future price movements. These models often combine points 1 and 3. I like most other people in this space have a collection of these, some better than others.

Given that I already have models in categories 3 and 4, am interested in a new model based on cointegration — not cointegration for pairs trading, but using the strong error-correcting relationships in a network of assets to determine likely next period moves.

Amongst a number of approaches for determining error-correcting relationships, have found the eigenvectors implied by the Johansen maximum likelihood estimate of the VECM to be the most stable as compared to other alternatives:

- heuristic zero crossings maximization
- beta estimates from rolling OLS regressor
- Various Ornstein-Uhlenbeck models (though with a particle filter the degree of noise can be reduced significantly)

I’m not going to state what I am doing right now, but may write up parts of it along the way.

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iirc, jml eigenvectors are the beta coint vectors; so, emphasizing stability implies you are seeking groups (or subgroups) which have consistent mutual cointegrating interrelationships, thus expecting to translate into (more) stable next period estimates?

A model with stable parameters (including betas implied by the eigenvectors in this case) allows a higher degree of confidence from period to period. I use information from the ECM model not for pairs trading, but for a more general analysis of the asset movements.

I may end up using a more sophisticated state based model, but for now want to see where this goes.

Makes sense, thanks for clarifying. Look forward to seeing where you go; seems either dispersion or index convergence are natural avenues, given good subgroup dynamics model.