A1159
Title: Inference in matrix-valued time series with common stochastic trends and multifactor error structure
Authors: Greta Goracci - Free University of Bozen/Bolzano (Italy) [presenting]
Rong Chen - Rutgers University (United States)
Lorenzo Trapani - University of Leicester (United Kingdom)
Simone Giannerini - University of Udine (Italy)
Abstract: The aim is to develop an estimation methodology for a factor model for high-dimensional matrix-valued time series, where common stochastic trends and common stationary factors can be present. The focus, in particular, is on the estimation of (row and column) loading spaces, of the common stochastic trends and of the common stationary factors, and the row and column ranks thereof. In a set of (negative) preliminary results, it is shown that a projection-based technique fails to improve the rates of convergence compared to a flattened estimation technique, which does not take into account the matrix nature of the data. Hence, a three step algorithm is developed where: (i) the data is first projected onto the orthogonal complement to the (row and column) loadings of the common stochastic trends; (ii) such trend free data is subsequently used to estimate the stationary common component; (iii) the estimated common stationary component is removed from the data, and re-estimate, using a projection-based estimator, the row and column common stochastic trends and their loadings. It is shown that this estimator succeeds in refining the rates of convergence of the initial, flattened estimator. As a byproduct, consistent eigenvalue ratio-based estimators are developed for the number of stationary and nonstationary common factors.
