 Strong mixing of a stationary process

Let ${\mathcal{F}}_{-\infty }^0$ and ${\mathcal{F}}_n^{\infty }$ be the sigma-algebras generated by the past and future observations. The mixing coefficient is $\alpha (n)={\sup }_{A\in {\mathcal{F}}_{-\infty }^0,B\in {\mathcal{F}}_n^{\infty }}|P(A\cap B)-P(A)P(B)|$. Strong mixing means $\alpha (n)\to 0$. Appropriate quantitative mixing and moment conditions can imply a central limit theorem; absolute summability of autocovariance alone does not.