The exact likelihood function of a Gaussian vector autoregressive-moving average (VARMA) model is evaluated in two nonstandard cases: (a) a parsimonious structured form, such as obtained in the echelon form structure or the scalar component model (SCM) structure; (b) a partially nonstationary...

The aim of this work is to investigate the effects of temporal aggregation and systematic sampling on periodic autoregressive moving average (PARMA) time series. Firstly, it is shown that the class of weak PARMA processes, i.e. with uncorrelated but possibly dependent errors, is closed under...

The exact Fisher information matrix of a Gaussian vector autoregressive-moving average (VARMA) process has been considered for a time series of length N in relation to the exact maximum likelihood estimation method. In this paper it is shown that the Gaussian exact Fisher information matrix...