Calculation of the fisher information matrix for periodic ARMA models

The present article is mainly concerned with the calculation of the Fisher information matrix associated to a periodic autoregressive moving average model (P-ARMA). We provide a computation algorithm based on the conditional likelihood function expression. The established algorithm extends Klein and Melard's algorithm (1989) elaborated for the classical ARMA models, to the case of periodic autoregressive moving average models. Moreover, for the application of this algorithm, we provide a procedure to compute the theoretical periodic autocovariance function in terms of the parameters of the periodic model. In addition, we give a necessary and sufficient condition for non singular Fisher information matrix of a periodic ARMA model.