Sufficient statistics for arma models with some fixed parameters
Sahib Esa, Georgi N. Boshnakov · Communication in Statistics- Theory and Methods · 1998
The likelihood function of ARMA processes with some fixed parameters is considered. An expression for it and a sufficient statistic are obtained. It is shown how the proposed approach can be used to obtain closed form expressions for the likelihood functions of some ARMA models. Applications to parameter estimation, hypothesis testing, speech processing and related problems are discussed.