The authors consider estimates of the correlation parameter \(\rho\) of a first order autoregression process \(X_ t\) whose innovation distribution F(x) is supported either on \(x\geq 0\) (positive) or on -1\(\leq x\leq 1\) (finite interval). F(x) is assumed to be regularly varying at the endpoints of the support with exponent \(\alpha\), namely at zero: \[ \lim_{t\downarrow 0}F(tx)/F(t)=x^{\alpha}\quad for\quad all\quad x>0. \] Estimators like \({\hat \rho}{}_ n=\min_{1\leq t\leq n}x_ t/x_{t+1}\) (for F(x) positively supported) motivated by extreme value theory are introduced. These estimates are sometimes reasonably better than analytically difficult maximum likelihood estimators. In the case of exponential distribution F(x) the maximum likelihood estimator will be equal to \({\hat \rho}{}_ n\). The proofs of the main result rely heavily on point process methods from extreme value theory.