A seasonal fractional multivariate model. A testing procedure and impulse responses for the analysis of GDP and unemployment dynamics

This paper deals with the analysis of seasonally, fractionally integrated, multivariate models. We present a procedure that permits us to test the seasonal fractional differencing parameters from the reduced-form system, which allows us to recover the parameters of the structural model through simple restrictions as in the standard VAR case with the additional incorporation of seasonality and fractional integration. An empirical application based on a bivariate system using GDP and unemployment in the UK, USA and Japan is also carried out at the end of the paper.