First Order Autoregressive Processes and Strong Mixing

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).