The embedment of co-integration in time series analysis : problems and cases for single equation approach to exchange rate modelling

In this thesis, the long-run Purchasing Power Parity model and the Flexible Price Monetary Approach to the exchange rate are studied. The purchasing power parity (hereafter the PPP) model is a two country model and basically assumes that, the same goods or basket of goods should sell for the same price in any two countries when measured in a common currency. This implies that the exchange rate depends upon the price levels. Similarly, the flexible price monetary approach (hereafter the FPMA) is also a two country model, however, it assumes that the exchange rate is influenced by relative money supplies, relative income and relative interest rates instead of the relative price levels. These models are examined via the estimation of a single equation using co-integration analysis techniques developed by Engle and Granger (1987). Co-integration is a very powerful and reliable technique in investigations involving non-stationary series. By their nature, non-stationary series fluctuate up and down away from their mean, implying that they have the tendency to possess different mean at different point in time. However, the linear combination of two or more non-stationary series integrated of the same order (have the same property) is expected to change to stationary (stability), and co-integration technique was developed to achieve this transformation (change non-stationary series to stationary series). The Engle and Granger (1987) two stage procedure for co-integration analysis has been widely applied in cases involving up to two variables (non-stationary time series). The present study involves more than two variables in a single equation. Therefore it makes an original contribution to the literature in that it has successfully applied the single equation approach widely used for estimations of up to two variables. Thus, the study provides a bridge between the conventional approaches that adopt standard testing procedures, and the more recent sophisticated approaches that adopt multivariate equations or the full information maximum likelihood (FIML). Stationarity properties of individual series including exchange rates are analysed via a unit root test by means of both the Dickey Fuller (DF) and Augmented Dickey Fuller (ADF) procedures. The Lagrange Multiplier (LM) was applied to select an appropriate number of augmentations in the case of the ADF tests. When initially tested in levels, all series showed the property of non-stationary 1(1) variable, but were all changed to stationary variables when tested in first difference form. The period-by-period deviations of the models from their respective equilibrium positions are analysed via the error correction mechanisms (ECMs). The ECMs encompass the variables of the short-run dynamic model as well as those of the long-run static model, all of which are estimated in a single error correction equation. The robustness of this approach (single equation estimation) shed a great light on the treatment of the PPP model and FPMA respectively as long-run models of exchange rate determination.