Abstract: We provide a parametrization of Vector Autoregression (VAR) that enables one to look  at  the  parameters  associated  with  unit  root  dynamics  and  those  associated  with stable dynamics separately.  The task is achieved via a factorization of the VAR polynomialthat partitions  the  polynomial  spectrum  into  unit  root  and  stable  and  zero  roots  via  polynomial factors.   The  proposed  factorization  adds  to  the  literature  of  spectral  factorization  of  matrix polynomials.   The  main  benefit  is  that  using  the  parameterization,  actions  could  be  taken  to model  the  dynamics  due  to  a  particular  class  of  roots,  e.g.   unit  roots  or  zero  roots,  without changing  the  properties  of  the dynamics  due  to  other  roots.   For  example,  using  the  parameterization one is able toestimate cointegrating space with appropriate rank that maintains the root  structure  of  the  original  VAR  processes  or  one  can  estimate  a  reduced  rank  causal  VAR process maintainingthe constraints of causality.  In essence, this parameterization provides the practitioner anoption to perform estimation of VAR processes with constrained root structure (e.g.,  conintegrated VAR  or  reduced  rank  VAR)  such  that  the  estimated  model  maintains  the assumed rootstructure.

This is a joint work with Ticker McElroy