Analysis of cointegrated macroeconomic time series

Abstract

The tradition of using the sample autocorrelation and partial autocorrelation functions to determine whether a series is stationary or otherwise, has become a thing of the past. In this modem era, testing for a unit root has become a common starting point in applied time series analysis. The consequences of ignoring this procedure have been documented in the literature. Various unit root estimation techniques have been discussed several authors. Most commonly applied unit root test procedures have been the Augmented Dickey-Fuller (ADF) and Phillips-Perron tests due to Dickey and Fuller (1979) and Phillips and Perron (1988). A frequency domain approach due Akdi and Dickey (1998) and Evans and Dickey (1998) have also been found to be effective. An application of a unit root test using local data on Leading Indicator Indices (Lil) for South Africa established that the series contains a unit root and hence is non-stationary. We have also considered the situation where the series might be seasonally nonstationary. Seasonal unit root tests were discussed with special attention to quarterly data. Again, an application of this concept using monthly U.S. liquor consumption data confirmed the presence of a seasonal unit root. Unit root tests form the bedrock of the concept of cointegration. The concept of cointegration and error correction model (ECM) has come to play an important role in much of macroeconomic time series analysis in recent years. Financial statisticians as well as econometricians, in much of their work, may want to find out whether there is a long-run relationship among variables. Some tests have been developed in the literature and some of these have been discussed in this study. The Engle-Granger method is preferable when the analysis involves two time series data. Our aim to conduct an empirical research into the efficiency of the Phillips-Ouliaris cointegrating test via the OLS and Yule-Walker methods also revealed that the test performs better when the Yule-Walker method is used instead of the OLS method. A

numerical example of the Engle-Granger, Cointegrating Regression Durban-Watson, and Phillips-Ouliaris methods using data on money supply (Ml) and amount of coin and banknotes in circulation in South Africa showed that the two series are indeed cointegrated, hence the existence of a long-run equilibrium relationship between these variables. In the multivariate context, the Johansen cointegrating test is most appropriate. An application of the Johansen cointegration test using monthly data on exchange rates of the rand to the British pound and the U.S. dollar established a long-run relationship between these variables. 6.2 Suggestions for Fur1her Research We suggest the use of the Bootstrap methods to investigate the performance of any of the cointegration tests discussed in this study, more importantly to investigate the performance of the Phillips-Ouliaris cointegration test via the OLS and Yule-Walker methods. Results can then be compared with those obtained using Monte Carlo methods.