Nonstationary dynamic factor analysis

In this paper, we present a procedure to build a dynamic factor model for a vector of time series. We assume a model in which the common dynamic structure of the time series vector is explained 11 through a set of common factors, which may be nonstationary, as in the case of common trends. Identification of the nonstationary I( d)factors is made through the common eigenstructure of the 13 generalized covariance matrices, properly normalized. The number of common nonstationary factors is the number of nonzero eigenvalues of the above matrices. A chi-square statistic is proposed to test 15 for the number of factors, stationary or not. The estimation of the model is carried out in state space form. This proposal is illustrated through several simulations and a real data set. 17

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