  The present paper, characterizes the invertibility and causality conditions
of a periodic ARFIMA (PARFIMA) models. We first, discuss the conditions in the
multivariate case, by considering the corresponding p-variate stationary ARFIMA
models. Second, we construct the conditions using the univariate case and we
deduce a new infinite autoregressive representation for the PARFIMA model, the
results are investigated through a simulation study.
