Inference in small cointegrated systems: some Monte Carlo results
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The Johansen procedure for testing and estimating cointegration models is analysed from a practitioner's perspective. We adress the robustness of the cointegration tests in small samples and with respect to particular types of misspecification of the model. A small cointegrated system is parameterized and forms the basis for the Monte Carlo simulations. Non-parametric estimates of the distribution of the Trace and )- Max tests are reported, as well as for some of the estimators for long- and short-run parameters in the model respectively. Power properties and finite sample performance for the cointegration test and estimators are discussed and the results are interpreted in the light of available asymptotics. The types of model misspecification considered include the case with wrong dynamic specification (i.e. wrong order k in the VAR model) and the case when we ignore non-normality in the DGP residuals (i.e. when the DGP residuals are subject to ARCH (Auto Regressive Conditional Heteroscedasticity) or are serially correlated). We also discuss how data properties like temporal aggregation or systematic sampling may affect the inference on cointegration, and how the Johansen procedure performs under those conditions. Finally, we consider the case with cointegration between non-stationary latent variables which are observed with measurement errors.