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DIFFERENTIAL GEOMETRY OF ARMA MODELS
Author(s) -
Ravishanker Nalini,
Melnick Edward L.,
Tsai ChihLing
Publication year - 1990
Publication title -
journal of time series analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.576
H-Index - 54
eISSN - 1467-9892
pISSN - 0143-9782
DOI - 10.1111/j.1467-9892.1990.tb00057.x
Subject(s) - mathematics , autoregressive–moving average model , exponential family , estimator , autoregressive model , statistic , likelihood ratio test , statistical hypothesis testing , statistics , statistical inference , inference , test statistic , artificial intelligence , computer science
. A general approach for the development of a statistical inference on autoregressive moving‐average (ARMA) models is presented based on geometric arguments. ARMA models are characterized as members of the curved exponential family. Geometric properties of ARMA models are computed and used to suggest parameter transformations that satisfy predetermined properties. In particular, the effect on the asymptotic bias of the maximum likelihood estimator of model parameters is illustrated. Hypothesis testing of parameters is discussed through the application of a modified form of the likelihood ratio test statistic.