Stochastic unit root models

This paper develops a dynamic switching model, with a random walk and a stationary regime, where the time spent in the random walk regime is endogeneously predetermined. More precisely, we assume that the process is recursively defined by Y_t = μ + Y_t-1 + ε_t, with stochastic probability π_rw(Y _t-1), Y_t = μ + ε_t, with stochastic probability 1 - π_rw(Y_t-1), where (ε_t) is a strong white noise and π_rw is a nondecreasing function. Then, the dynamics of the process (Y_t), its marginal distribution, and the distribution of the time spent in the unit root regime depend on the pattern of random walk intensity π_rw and on the noise distribution F. Moreover, we study the links between the endogeneous switching regime and the degree of persistence of the process (Y_t).