The aim of this study is to discuss the properties of squares of a pure diagonal bilinear (PDBL) time series model and how these properties can be used to distinguish between a linear (ARMA) model and a non-linear (bilinear) model. We showed that for the Pure diagonal bilinear process, the square of the series have the same covariance structure as an ARMA process. Simulated data was used to illustrate the results obtained in this study.