This paper analyzes a novel source of long memory though multicollinearity. We consider a vector autoregression of order one, a VAR(1) of large dimension. We use a final equation representation to show that as the VAR dimension tends to infinity while the proportion of stochastic trends remains constant, individual variables may exhibit strong persistence akin to fractional integration whose degree corresponds to the fraction of unit roots in the system. We consider the implications of our findings for the volatility of asset returns where the so- called golden-rule of realized volatility states that they always exhibit fractional integration of degree close to 0.4. Hence, this empirical feature can be related to the correlation of the many financial assets.
CHEVILLON, G., HECQ, A. and LAURENT, S. (2014). Persistence Through Correlation. In: 15th OxMetrics User Conference.