Publication: Threshold stochastic unit root models
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2002-09
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Abstract
This paper introduces a new class of stochastic unit root (STUR) processes, where the randomness of the autorregresive unit root is driven by a threshold variable. These new models, the threshold autorregresive stochastic unit root (TARSUR) models, are stationary in some regimes and mildly explosive in others. TARSUR models are not only an alternative to fixed unit root models but present interpretation, estimation and testing advantages with
respect to the existent STUR models. The paper analyzes the stationarity properties of
the TARSUR models and proposes a simple t -statistic for testing the null hypothesis of a fixed unit root versus a stochastic unit root hypothesis. It is shown that its asymptotic distribution (AD) depends on the knowledge we have about the threshold values: known, unknown but identified, and unknown and unidentified. In the first two cases the AD is a standard Normal distribution, while in the last one the AD is a functional of Brownian Motions and Brownian Sheets. Monte Carlo simulations show that the proposed tests behave very well in finite samples and that the Dickey-Fuller test cannot easily distinguish
between an exact unit root and a threshold stochastic unit root. The paper concludes with applications to stock prices and interest rates where the hypothesis of a fixed unit root is rejected in favor of the threshold stochastic unit root.