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This paper studies cointegrated systems of multiple time series which are individually well described as integrated processes (with or without a drift). Necessary and suﬀicient conditions for cointegration are given. These conditions form the basis for a new class of statistical procedures designed to test for cointegration. The new procedures rely on principal components methods. They are simple to employ and they involve only the standard normal distribution. Monte Carlo simulations reported in the paper indicate that the new procedures provide simple and apparently rather powerful diagnostics for the detection of cointegration. Some empirical applications to macroeconomic data are conducted.
Phillips, Peter C.B. and Ouliaris, Sam, "Testing for Cointegration Using Principal Component Methods" (1986). Cowles Foundation Discussion Papers. 1052.