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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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