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

Valentina Corradi

29 citations0/0 files storedEconometric Theory

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Monetary Policy and Economic Impact Complex Systems and Time Series Analysis Diverse Scientific and Economic Studies

Abstract

We construct properly scaled functions of Rp-valued partial sums 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 bound 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.

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References

1992Testing the null hypothesis of stationarity against the alternative of a unit root 2007Brownian Motion and Stochastic Calculus 1991Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation 1994Automatic Lag Selection in Covariance Matrix Estimation 1992Consistent Covariance Matrix Estimation for Dependent Heterogeneous Processes 1994Posterior Odds Testing for a Unit Root with Data-Based Model Selection 2003Strong rules for detecting the number of breaks in a time series 1994Deciding between I(1) and I(0)

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