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Exact Geometry of Autoregressive Models
Author(s) -
Garderen Kees Jan van
Publication year - 1999
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 - 10.1111/1467-9892.00122
Subject(s) - mathematics , autoregressive model , covariance matrix , star model , curvature , statistic , covariance , statistics , geometry , autoregressive integrated moving average , time series
Exact expressions for the statistical curvature and related geometric quantities in first‐order autoregressive models are derived. We present a method for calculating moments that is applicable in general autoregressive models. It combines the algebra of differential and difference operators to simplify the problem, and to obtain results valid for all sample sizes. The exact covariance matrix for the minimal sufficient statistic is also derived.