Change‐Point Estimation of Fractionally Integrated Processes

Abstract

In this paper we analyze the least‐squares estimator of the change point for fractionally integrated processes with fractionally differencing parameter −0.5 < d < 0.5. When there is a one‐time change, we show that the least‐squares estimator is consistent and that the rate of convergence depends on d . When there is no change, we find that the least‐squares estimator converges in probability to the set {0, 1} for −0.5 < d ≤ 0 but is likely to suggest a spurious change for 0 < d < 0.5. Simulations are also used to illustrate the asymptotic analysis.