Journal of Time Series Analysis

Change‐Point Estimation of Fractionally Integrated Processes

Journal Article

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.

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