Parameter estimation for noncausal and heavy-tailed autoregressive processes

The study of finite variance autoregressive (AR) processes has resulted in a mature and well developed body of theory, however, many processes are not described well by finite variance models. In this dissertation, two techniques are examined for the estimation of the parameters of an AR process with infinite variance.; The α-stable distributions are one of the more popular distributions used for modelling infinite variance processes. The first estimation technique examined is a maximum likelihood estimator based upon the α-stable distribution. The asymptotic properties of this estimator for the parameters of an AR model are derived. The estimator is then extended to include the parameters of the underlying α-stable distribution. The asymptotic properties of this combined estimator are also derived.; The second estimation technique is referred to as the minimum entropy estimator. Oddly enough, considering the infinite variance setting, this estimator is based on higher order sample moments of the observed AR process. Some asymptotic results concerning this estimator have been previously discovered. In this dissertation significant refinements of these results are made.; The asymptotic results derived for the two estimators are based upon point process techniques. These methods provide elegant solutions to what are otherwise intractable problems. The study of the maximum likelihood estimator is accomplished by the application of a known point process result. The study of the minimum entropy estimator requires the derivation of a new point process result.; Both of these estimators can be used when the AR process under study is noncausal. Some series exhibit patterns that cannot be captured by causal AR models. By removing the causality restriction, it is possible that a series can be adequately explained by a non-causal AR model, and not require recourse to a more elaborate modelling method.; The two estimation techniques are compared at the end of the dissertation using a variety of simulations. In addition, the techniques are used to model stock volume series for several different securities.