Guaranteed parameter estimation in a first order autoregressive progress with infinite variance

Abstract

Let be a first order autoregressive process where the ε_t's are independent identically distributed random variables. The distribution of ε₁ is assumed to be symmetric and asymptotically Pareto of index p for some p ε (1,2). The variance in this case is infinite but for any r < p the absolute moment of order r is finite. At first, for r ε (1, p], we introduce an appropriate weighted least squares estimator of the autoregression parameter λ. It is shown that it is strongly consistent whatever is the true value of λ. Then a sequential procedure based on a modification of this estimator is proposed. It enables to achieve a prescribed precision measured by the r th order absolute moment of the estimation error

Keywords:

• autoregression parameter
• asymptotically Pareto distribution
• sequential estimation
• prescribed precision