STATISTICAL ANALYSIS AND TESTING OF COINTEGRATED SYSTEMS

Abstract

This paper deals with estimation and testing for cointegration when deterministic trends are present in the data generating process. The study confirmed that to estimate the Vector Error Correction Model (VECM) when there is no cointegration will produce an egregious pitfall. Derivation of the linkage between the residual matrix of VECM and the corresponding eigenvalues of the product moment matrices is provided. The bivariate system designed shows a reversal relationship between the lag-lenghts and the values of the likelihood ratio (LR) statistic. Moreover, the values of the (LR) test for different lags at various sample sizes are reported in the simulation. The Monte Carlo experiment shows that the null hypothesis of no cointegration is rejected in favours of cointegration inspite of the deterministic trend in the data. The standard Z-test and t-test prove to be more robust via size properties for a wider range of nuisance parameter than the coefficient based tests.


KEY WORDS: Cointegration, Deterministic trend, Vector Autoregressive Estimates, Hypothesis Testing and Data generation process(DGP).


Global Jnl of Mathematical Sciences Vol. 31) 2004: 11-21