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The effects of \(I(1)\) series on cointegration inference. (English) Zbl 1035.62093
Summary: Under traditional cointegration tests, some eligible \(I(1)\) time series systems \(X_t\), that are not cointegrated over a given time period, say \((0,T_1]\), sometimes test as cointegrated over sub-periods. That is, the system appears to have a stationary linear structure \(\xi'X_t\) for a certain vector \(\xi\) in the period \(0<t\leq T_1\). Understanding the dynamics between cointegration test power and restricted sample size that causes this inversion of results is a crucial issue when forecasting over extended future time periods.
We consider non-cointegrated systems that are closely related to collinear systems. We apply a residual based procedure to such systems and establish a criterion for making the decision whether or not \(X_t\) can be continuously accepted as \(I(0)\) for \(t>T_1\) when \(X_t\) was accepted as \(I(0)\) for \(t\leq T_1\).
MSC:
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
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