Identifying the finite dimensionality of curve time series
by Neil Bathia
Abstract: The curve time series framework provides a convenient vehicle to accommodate some nonstationary features into a stationary setup. We propose a new method to identify the dimensionality of curve time series based on the dependence between adjacent curves. The practical implementation of our method boils down to eigenanalysis of a real matrix. Furthermore, determination of the dimensionality is equivalent to identifying the number of non-zero eigenvalues of this matrix, which we carry out in terms of some bootstrap tests. Asymptotic properties of the proposed method are investigated. In particular, our estimators of the zero-eigenvalues enjoy the fast convergence rate n while the estimators of the non-zero eigenvalues converge at the standard root-n rate. The proposed methodology is illustrated with both simulated and real data sets.
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