Date of Award


Degree Type


Degree Name

Master of Applied Science


Faculty of Science and Technology

First Advisor

Associate Professor James Cross


In this thesis the state space approach and the Kalman recursions are used for modelling univariate time series data. The models that are examined in this thesis are time varying Coefficient Autoregressive models, which can be represented in state space form. The coefficients are assumed to change according to a stationary process, a non-stationary process or a random process. In order to be able to estimate these changing unknown coefficients, they will be treated as state variables and the equation describing the changes of the state variables will be given by the state equation. The model can then be expressed in the form of a measurement equation. The parameters of the model, which include the transition matrix T, the covariance matrices of the random terms in the state equation and the measurement equation denoted respectively by Q and R will be obtained using the EM algorithm developed by Shumway and Stoffer (1982). Other models considered for comparison in this thesis are the Box-Jenkins and Harvey's Structural models. The results of model fitting are illustrated by applying these three models to three special data sets. These results are compared to investigate whether the time varying coefficients model can provide a better fit, and, where appropriate, a suitable data -transformation is applied to the data sets in order to get a fit of the time varying coefficient autoregressive model.

Included in

Mathematics Commons