Estimation for first-order autoregressive processes with positive or bounded innovations

AbstractWe consider estimates motivated by extreme value theory for the correlation parameter of a first-order autoregressive process whose innovation distribution F is either positive or supported on a finite interval. In the positive support case, F is assumed to be regularly varying at zero, whereas in the finite support case, F is assumed to be regularly varying at the two endpoints of the support. Examples include the exponential distribution and the uniform distribution on [−1, 1 ]. The limit distribution of the proposed estimators is derived using point process techniques. These estimators can be vastly superior to the classical least squares estimator especially when the exponent of regular variation is small