L 1common trend filtering: an extension

Abstract

common trend filtering enables us to estimate a common continuous piecewise linear trend and the corresponding factor loading coefficients of multiple time series simultaneously. In this paper, we extend this by replacing the identifying restriction with an alternative identifying restriction and develop an algorithm for solving this new problem. As the new identifying restriction is linear, it can include other linear restrictions of parameters. Using this modification, e.g. we can estimate the vector of the factor loading coefficients so that its two entries will equal, which current common trend filtering cannot handle. We also provide a way of specifying the tuning parameter of the new problem and empirically illustrate how well the algorithm works.