# Finding relationships between assets that can be used for statistical arbitrage

Instead of focusing on predicting price direction and price volatility with nonlinear models derived with machine learning methods, an alternative would be to try and discover exploitable price relationships between assets of the same class and react (=trade) when mispricing happens, in other words, do statistical arbitrage. In a sense this is somehow ‘easier’ than attempting to forecast prices, since the only thing one has to do is to find a relatively stable, linear or non-linear relationship between a group of at least two assets and assume that, from the time of its detection, that relationship will carry on for some time into the future. Trading under this assumption is then very much a reactive process that is triggered by price movements that diverge significantly from the modeled relationship. Traditional Pair Trading and trading of assetts in a VECM (Vector Error Correction Model) relationship are good examples for statarb using linear models. So why not use a simple one-layer neural network or even an RBM to discover a non-linear price relationship between two not-cointegrated assets and if this discovery process is successful, trade it in a similar way to a classical pair ? Things become even more interesting when groups with more than just two assets are considered. This would then be the non-linear equivalent of a VECM.