A0292
Title: Rank and factor loadings estimation in time series tensor factor model by pre-averaging
Authors: Clifford Lam - London School of Economics and Political Science (United Kingdom) [presenting]
Abstract: A pre-averaging method is introduced for tensor time series data to estimate factor loadings matrices and the rank of the core tensor for a time series tensor factor model. Without the knowledge of either the rank or the factor loading matrices, we pre-average the fibres of an unfolded tensor and systematically search for one that maximizes the signals from the factors. Projection directions corresponding to the ``strongest'' factors for each mode of the tensor are then obtained. These directions are then used to re-estimate the rank of the core tensor and all factor loadings matrices. Rates of convergence of these estimators are spelt out, all under a set of econometrics assumptions for the factors and the noise of the tensor data, allowing serial correlations in the noise as well as cross-correlations among noise fibres. Our proposed method bypass the difficulty of proving that the estimated factor loadings matrices produced from the usual HOOI converge to the true underlying ones even under the i.i.d. noise setting. Simulation results show the effectiveness of our method compared to other state-of-the-art ones. A set of real data is also analyzed.
