Degree Name

Master of Science (Hons.)


School of Mathematics and Applied Statistics


This thesis is concerned with a practical procedure of applying the Asymptotic Quasi-likelihood Method (AQLM) and involves the application of the AQLM in linear models as well as in estimating the fractional differencing parameter in fractional ARIMA(p, ci, models. The Quasi-likelihood Method (QLM) is an inference method which unifies the traditional methods of maximum likelihood (ML) and least squares (LS). The ML method, introduced by Fisher, is dependent upon knowledge of the entire form of the underlying distribution. The method of LS, developed by Gauss, focuses on minimising the sum of squares. The QLM follows the framework of the ML method but depends on weaker conditions as well as having a broader application than the ML method. The QLM is a common inference tool since it solves certain problems which may not be solved efficiently via the traditional methods of ML and LS. The AQLM, applied when the QLM is deemed inappropriate due to a lack of information on the process or due to the appearance of nuisance parameters, is rapidly becoming a popular inference method especially in the field of stochastic processes. There are two alternative directions in inference for stochastic processes. Firstly, there is the question of finite-sample optimality properties as opposed to asymptotics. Secondly, there is the question of methods which make no assumptions as to the true underlying distribution, i.e. second order methods such as LS and QL and more general semi-parametric methods.