where \(X_1(t),X_2(t),...,X_k(t)\) are the input time series to be considered as explanatory variables contributing to the temporal dynamics of the output series \(Y\left(t\right)\) and \(\eta(t)\) is a stationary random process. The terms \(\alpha_1(B), \alpha_2(B),..., \alpha_k(B)\)are fractional polynomials in the back-shift operator B (such that \(B^s(X(t))=X(t-s)\)) of the form: