THE JOHANSEN COINTEGRATION TECHNIQUE AND SPOT AND FORWARD RATE HYPOTHESIS

Abstract

Although the finite-sample properties of the Johansen Likelihood Ratio (LR) cointegration rank tests have been examined by some researchers, little has been done to study the finite-sample performance of the Johansen LR tests of linear restriction on the cointegrating vectors ?, and the adjustment coefficients ?. In Chapter 4, the Monte Carlo method is used to study the finite sample properties of these Johansen LR tests. The small finite-sample distributions of the Johansen LR tests are first examined. Their finite-sample performances are further examined under the deviation from normality of the residuals. And finite-sample biases due to the over-parameterization or incorrect deterministic components in the statistical testing models are investigated. I also study the power of these LR tests when the finite sample sizes are very small. The first part of the Chapter 5 is an empirical application of the Johansen procedure to test cointegration between spot and contemporaneous forward rate as well u cointegration between spot and lagged forward rate. Inferences based on the Johansen technique are also made to test the unity of the cointegrating vector and the exogeneity of spot and the forward rate. Cointegration is found for the two types of spot and the forward rate relations. While the spot rate is exogenous in the cointegration of spot and lagged forward rate, both the spot and the forward rate are, however, not exogenous in the cointegration of spot and contemporaneous forward rate. I also demonstrate that when two variables are cointegrated, it is invalid to make inference on the level relationship, using corresponding "change" model, arrived at by deducting the lag-one period value of the dependent variable from the both sides of their level equation. Monte Carlo simulation is again employed to generate, two non-stationary variables, which are cointegrated with unit cointegrating vector. I applied various "change" models to the generated data. More interestingly, when the “change" models are applied to the forward rate, the results are very similar to those obtained from the simulated data generated based on the cointegration between the contemporaneous variable. The findings suggest that the underlying cointegration relation of spot and the forward rate may exist between their contemporaneous levels, rather than between the spot and lagged forward rate, as assumed in the unbiased forward rate hypothesis. Chapter 6. I apply both the Engle and Granger procedure and Johansen technique and test the Purchasing Power Parity (PPP) hypothesis for seven Asia Pacific countries. In both cases of using Japan and Singapore as the base country, I find strong evidence in favour of PPP when the maximum likelihood approach is implemented. However, different results are obtained for some countries when Engle and Granger approach is applied. In addition, the null of unit cointegrating vector is rejected. It is found, not surprisingly, that when a prior restriction is included in the univariate testing model of Engle and Granger procedure, it is easier to find the non-stationarity of the regression residuals, which amounts to the rejection of the cointegration.