Limit theory for moderate deviations from a unit root with a break in variance

Consider the model y(t) = (n)y(t - 1) + u(t), t = 1, ..., n with (n) = 1 + c/k(n) and u(t) = sigma 1EtI{t k(0)} + sigma 2EtI{t > k(0)}, where c is a non-zero constant, sigma(1) and sigma(2) are two positive constants, I{ <bold> </bold>} denotes the indicator function, k(n) is a sequence of positive constants increasing to such that k(n) = o(n), and {E-t, t 1} is a sequence of i.i.d. random variables with mean zero and variance one. We derive the limiting distributions of the least squares estimator of (n) and the t-ratio of (n) for the above model in this paper. Some pivotal limit theorems are also obtained. Moreover, Monte Carlo experiments are conducted to examine the estimators under finite sample situations. Our theoretical results are supported by Monte Carlo experiments.