Abstract: We propose an intuitive and simple-to-use procedure for estimating the cointegration rank of a high-dimensional time series system with possible breaks. Based on a similar idea to a principal component analysis, the cointegration rank can be estimated by the number of eigenvalues of a certain nonnegative definite matrix. There are several advantages to the new method: (a) the dimension of the cointegrated time series is allowed to vary with the sample size; (b) it is model free; and (c) it is simple to use and robust against possible breaks in trend. The cointegration rank can be estimated without the need for a priori testing and estimating of the break points. The asymptotic properties of the proposed methods are investigated when the dimension of the time series increases with the sample size, which offers a new alternative to deal with high-dimensional time series. Finally, the proposed precedure is demonstrated by means of simulations.

Key words and phrases: Cointegration, eigenanalysis, high-dimensional time series, nonstationary processes, structural break.