DECIDING BETWEEN /(0) AND /(1) VIA FLIL-BASED BOUNDS

We consiruct properly scaled functions of R^p-valued partial sunns of demeaned data and derive bounds via the functional law of the iterated logarithm for strong mixing processes. If we obtain a value below or equal to the hound we decide in favor of I(0): otherwise we decide in favor of I(1). This provides a consistent rule for classifying time series as being I(1) or I(0). The nice feature of the procedure lies in the almost sure nature of the bound, guaranteeing a lim sup-type result. We finally provide conditions for the strong consistency of estimators of the variance in the dependent and heterogeneous case.