What multivariate approaches can tell us

I've focused on "univariate" strategies in the high frequency space for the last few years. Recently I did some work on medium/long term strategies for the Canadian market. In the course of investigation realized that I've been ignoring information by just focusing on signals using a single asset and not looking at related assets to provide additional signal.

Of course it has always been in the back of my mind to diversify into strategies of more than one asset. But even if one intends to trade single securities, the information that other related assets or indicators can provide gives us an edge. In particular I need to be looking at:

• Multivariate SDEs with jointly distributed series
  In the simplest case this is expressed in covariance, but covariance is just one of the moments of relationships.
  
  
• Economic signals (well for medium / long term)
  
  
• Cointegration relationships
  Not only linear relationships but quadratic. These need to be tested carefully in and out of sample
  

My initial successes with Canadian strategies underscored how effective multivariate signals can be.