Modelling heteroscedasticity in exchange rates for the Maltese lira

Abstract

In this dissertation we shall consider the different stages involved in modelling empirical time series. We shall first look at the theory of multivariate ARMA models. We shall also look at the theory of unit root processes and discuss briefly some of the some of the most popular unit root tests available in literature. A detailed discussion of the theory of ARCH model and a brief description of the GARCH model is also provided. An extensive time series analysis is applied to study the exchange rates constituting the currency basket to which the Maltese Lira is pegged. These rates are the Euro, the Sterling and the Dollar. Our aim shall be to try to fit an adequate time series model to our data. First we fit a multivariate ARMA model to the log return series of the three rates and show that it is not satisfactory on a number of criteria. Next we shall apply the unit root tests to the Euro exchange rate after applying a natural log transformation to the series and thus show that the Euro exchange rate can be considered to be a unit root process. Finally we estimate an ARCH and a GARCH model for the log return series of the Euro exchange rate and show that from the three models considered in this dissertation these conditional heteroscedastic models are the best for modelling data such as ours.