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Summary We propose a likelihood ratio scan method for estimating multiple change points in piecewise stationary processes. Using scan statistics reduces the computationally infeasible global multiple‐change‐point estimation problem to a number of single‐change‐point detection problems in various local windows. The computation can be efficiently performed with order O{npt log (n)}. Consistency for the estimated numbers and locations of the change points are established. Moreover, a procedure is developed for constructing confidence intervals for each of the change points. Simulation experiments and real data analysis are conducted to illustrate the efficiency of the likelihood ratio scan method.

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This article studies the empirical likelihood method for long-memory time series models. By virtue of the Whittle likelihood, one obtains a score function that can be viewed as an estimating equation of the parameters of a fractional integrated autoregressive moving average (ARFIMA) model. This score function is used to obtain an empirical likelihood ratio which is shown to be asymptotically chi-square distributed. Confidence regions for the parameters are constructed based on the asymptotic distribution of the empirical likelihood ratio. Bartlett correction and finite sample properties of the empirical likelihood confidence regions are examined.