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multivariate approach OU approach

1. normalize return
   $p=\frac{p-E [p] }{ \sigma }$
2. how to find the pairs?
   OLS and find the min squared error.
   max correlation of two normalized time series.
3. trading signal
   when the absolute distance is larger than threshold, long the lower price one and short the higher price one.
4. problem
   maybe only one is badly priced. there is no mechanism to prevent buying badly priced stocks.

1. idea is if we find multivariate relations, it is less likely we buy a badly priced stock.