Improving cointegration tests under structural breaks in multivariate GARCH models

In time series, data may experience a sudden change / break in its dynamics. That is, there may be breaks in the mean, slope, trend function or some other characteristics that occur at random times. Structural changes may occur in time series due to policy changes, financial crises and natural disasters. Another destructive attribute is heteroscedasticity of error term. Econometric and financial time series are well known with a fat-tailed distribution that has the large skewness and/or excess kurtosis. The existence of the structural breaks and heteroscedastic error term may cause various problems such as biased, inconsistent estimations and poor predictions. Many studies demonstrated that heteroscedaticity and structural breaks in a cointegration relationship significantly influence the performance of cointegration tests. This dissertation proposes a more powerful test among residual based test, the new test's name is the "RALS(2)-LM GARCH", which is suitable for GARCH effects under the level or/and slope structural breaks. The test formed using the residual based Lagrange Multiplier method. New test relieves the practitioners from conducting extra analyses by considering the structural breaks and heteroscedasticity together. The proposed tests lies in the invariance feature that the distribution does not depend on the different values of GARCH parameter in the presence of multiple level and trend-breaks. The suggested test is adaptable to multiple breaks and heteroscedatic error terms. In simulation study, the performances of Engle-Granger (1987), Gregory-Hansen (1996), Westerlund-Edgerton LM (2007) and RALS(2)-LM GARCH are examined under structural break and GARCH effect. When the results of the simulation are examined in general, it can be argued that when there is a structural break in the series, the RALS(2)-LM GARCH and WE-LM test yielded better results. In addition, simulation result showed that GH test exhibits a liberal behavior and diverges from the nominal size while the EG test has more conservative results in different break scenarios. Furthermore, the simulation shows that the newly suggested RALS-based cointegration tests utilizing higher moment conditions exhibit substantial power gains even if the errors are GARCH distributed. Final evidence from the simulation study is that the position of the break and the type of cointegration model in the experiment design influenced the performances of the tests.