A Note on Mixing in High Dimensional Time series
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Various mixing conditions have been imposed on high dimensional time series, including the strong mixing (α-mixing), maximal correlation coefficient (ρ-mixing), absolute regularity (β-mixing), and ϕ-mixing. α-mixing condition is a routine assumption when studying autoregression models. ρ-mixing can lead to α-mixing. In this paper, we prove a way to verify ρ-mixing under a high-dimensional triangular array time series setting by using the Peason's ϕ^2, mean square contingency. Vector autoregression model VAR(1) and vector autoregression moving average VARMA(1,1) are proved satisfying ρ-mixing condition based on low rank setting.
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