Fitting dynamic fator models to nonstationary time series

Factor modelling of a large time series panel has widely proven useful\nto reduce its cross-sectional dimensionality. This is done by explaining common\nco-movements in the panel through the existence of a small number of common\ncomponents, up to some idiosyncratic behaviour of each individual series. To capture serial correlation in the common components, a dynamic structure is used as in traditional (uni- or multivariate) time series analysis of second order structure,i.e. allowing for infinite-length altering of the factors via dynamic loadings. In this paper, motivated from economic data observed over long time periods which show smooth transitions over time in their covariance structure, we allow the dynamic structure of the factor model to be non-stationary over time, by proposing a deterministic time variation of its loadings. In this respect we generalise existing recent work on static factor models with time-varying loadings as well as the classical, i.e. stationary, dynamic approximate factor model. Motivated from the stationary case, we estimate the common components of our dynamic factor model by the eigenvectors of a consistent estimator of the now time-varying spectral density matrix of the underlying data-generating process. This can be seen as time-varying principal components approach in the frequency domain. We derive\nconsistency of this estimator in a "double-asymptotic" framework of both cross-\nsection and time dimension tending to infinity. A simulation study illustrates the performance of our estimators.