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Abstract |
We seek for a contemporaneous linear transformation for a p-variate time series such that the transformed series is segmented into several lower-dimensional subseries, and those subseries are uncorrelated with each other both contemporaneously and serially. The method boils down to an eigenanalysis and, if p is large, a permutation in terms of maximum cross-correlations or FDR based on multiple tests. The asymptotic theory is established for both fixed p and diverging p when the sample size n goes to infinity, reflecting the fact that the method also applies when the dimension p is large in relation to n. Numerical experiements with both simulated and real datasets indicate that the proposed method is an effective initial step in analysing multiple time series data, which leads to substantial dimension-reduction in modelling and forecasting high-dimensional linear dynamical structures. |
