Cointegration is a dependence concept which is based on the observation that a linear combination of non-stationary assets that move together can be stationary. Cointegration has been used in the analysis of financial time series as well as in portfolio construction. The cointegration portfolio has been defined as the linear combination of assets which bests tracks a certain benchmark in the sense that its active returns are the most stationary.
Diversification can be understood as being invested in assets that move in opposite directions, as much as possible. Is the most diversified portfolio therefore the least stationary portfolio?