Structural breaks in dynamic factor models

In this thesis we analysed the problem of a single structural change occurring at some unknown data in multivariate time series. Our results rely on the assumption that the multivariate time series is generated by a dynamic factor model. Dynamic factor analysis is a very rich methodology which can be extended in many way to get a closer approximation to complex economic reality. They attempt to capture the correlation structure of a large number of original variables with a small set of common factors, in order to reduce the dimensionality of the vector space of the original variables. Three di_erent type of breaks has been analysed: the break in the mean level, the break in the factor loadings and the break in the factor moments. For each of them we suggest a model and therefore we focus the attention on the population and sample moments. When a break occurs, the data-generating process is not stationary anymore. The break in level affects the first moment of the process but the variance is still stationary whereas the other break types affect the second order moments. Furthermore we showed that the estimates are always affected by the break. Given these preliminary results we are interested in the Fourier transform of the estimated variance covariance matrices. For Geweke (1977) we know that all variation in the observed data may be decomposed into variance across frequencies using spectral techniques and, under some restrictions, much of the variation of the observable variables at low frequencies can be attributed to the common factors. Then, in order to investigate on the common factors number, we analyse the eigenvalues of estimated Fourier transform of the variance covariance matrices evaluated at frequencies close to zero. The target has been to understand if and in which way the break affects these matrices and their eigenvalues.