  Various mixing conditions have been imposed on high dimensional time series,
including the strong mixing ($\alpha$-mixing), maximal correlation coefficient
($\rho$-mixing), absolute regularity ($\beta$-mixing), and $\phi$-mixing.
$\alpha$-mixing condition is a routine assumption when studying autoregression
models. $\rho$-mixing can lead to $\alpha$-mixing. In this paper, we prove a
way to verify $\rho$-mixing under a high-dimensional triangular array time
series setting by using the Pearson's $\phi^2$, mean square contingency. Vector
autoregression model VAR(1) and vector autoregression moving average VARMA(1,1)
are proved satisfying $\rho$-mixing condition based on low rank setting.
