Abstract
We study estimation of the date of change in persistence, from I(0) to I(1) or vice versa. Contrary to statements in the original papers, our analytical results establish that the ratio-based break point estimators of Kim [Kim, J.Y., 2000. Detection of change in persistence of a linear time series. Journal of Econometrics 95, 97–116], Kim et al. [Kim, J.Y., Belaire-Franch, J., Badillo Amador, R., 2002. Corringendum to “Detection of change in persistence of a linear time series”. Journal of Econometrics 109, 389–392] and Busetti and Taylor [Busetti, F., Taylor, A.M.R., 2004. Tests of stationarity against a change in persistence. Journal of Econometrics 123, 33–66] are inconsistent when a mean (or other deterministic component) is estimated for the process. In such cases, the estimators converge to random variables with upper bound given by the true break date when persistence changes from I(0) to I(1). A Monte Carlo study confirms the large sample downward bias and also finds substantial biases in moderate sized samples, partly due to properties at the end points of the search interval.
Highlights
Studies of persistence change, i.e. series changing from I(0) to I(1) or vice versa, often employ ratio-based test procedures, originally proposed by Kim (2000), and further analysed by Kim et al (2002, KBA) and Busetti and Taylor (2004, BT)
The data generation process (DGP) is given in (1) and (2) with an intercept included in the regression, β = 5, εt ∼ N(0, 1) and the true break fractions are given by τ0 = {0.3, 0.5, 0.7}
This paper shows analytically that the ratio-based break fraction estimators of BT and KBA are not consistent for the true break point when mean effects have to be taken into account through a prior regression
Summary
I.e. series changing from I(0) to I(1) or vice versa, often employ ratio-based test procedures, originally proposed by Kim (2000), and further analysed by Kim et al (2002, KBA) and Busetti and Taylor (2004, BT). We provide representations of the limiting distributions of the KBA and BT break point estimators, (3) and (4), thereby showing that these ratio-based estimators are not consistent for the true break point when mean effects are taken into account. This problem arises from the contamination of otherwise stationary subsample observations by subtraction of a mean that covers some nonstationary values.
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