Exponential autocovariance decay of a causal autoregression ($|\gamma (h)|\le C{s}^{|h|}$)

The inverse autoregressive polynomial is an analytic function on a disk larger than the unit disk. The Cauchy estimate gives exponentially decaying coefficients of its infinite moving-average representation. Summing their products gives $|\gamma (h)|\le C{s}^{|h|}$ for some $s\in (0,1)$.