Title: About the parameterisation of hypertall transfer functions
Authors: Philipp Gersing - Vienna University of Technology (Austria) [presenting]
Abstract: A parameterisation theory is provided for what is called hypertall rational transfer functions $k(z)$ of dimension $(n\times q)$ with $n >> q$, where the entries are rational functions. Such transfer functions appear, for example, when modeling the common component of static and dynamic factor sequences. We introduce echelon realisations for so-called noise-free representations of hypertall transfer functions. In a noise-free realisation, no error term appears in the observation equation, as is the case in the usual parameterisations of factor model models. We relate the noise-free echelon realisation to the standard realisation and show that generically factor models follow an AR(1) process. The ultimate goal in applications is to use state space realisations where small errors in the autocovariance result in small errors in the ultimate purpose of the application, e.g. forecasting. The hope is that through a better understanding of the structure of hypertall transfer functions, we can come up with representations that result in better forecasting performance.