Threshold unit root models
AbstractOne of the main criticisms of unit root models is based on the theoretical fact that economic variables measured in rates cannot have unit roots. Nevertheless, standard unit root tests do not reject the existence of unit roots in many of those variables. In this paper we present a class of threshold models capable of replicating the behavior of economic variables such as unemployment, inflation and interest rates. Depending on the values of a threshold variable these models can have either a unit root or a stable root. However, despite the presence of the unit root, we prove they are stationary and geometrically ergodic. Least squares estimates of the parameters of these models are shown to be consistent and asymptotically normal. We propose the supremum of a e test in order to test the null of no threshold against the alternative of threshold when the threshold value is unknown. The limiting distribution is derived under the null of I (0) as well as under the null of 1(1). Critical values for both asymptotic distributions are computed and a finite sample study of the performance (size and power) of the tests developed in this paper is made. The paper concludes with an application to interest rates.
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Brownian motion; Brownian sheet; geometric ergodicity; hypothesis testing; threshold models; unit root processes;
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