A suﬀicient condition is given such that ﬁrst-order autoregressive processes are stong mixing. The condition is speciﬁed in terms of the univariate distribution of the independent identically distributed innovation random variables. Normal, exponential, uniform, Cauchy, and many other continuous innovation random variables are shown to satisfy the condition. In addition, an example of a ﬁrst-order autoregressive process which is not strong mixing is given. This process has Bernoulli (p) innovation random variables and any autoregressive parameter in (0, 1/2).
Andrews, Donald W.K., "First Order Autoregressive Processes and Strong Mixing" (1983). Cowles Foundation Discussion Papers. 897.