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Maximum likelihood estimation in space time bilinear models
Author(s) -
DAI YUQING,
BILLARD L.
Publication year - 2003
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 - 10.1111/1467-9892.00291
Subject(s) - mathematics , hessian matrix , bilinear interpolation , estimation theory , mathematical optimization , series (stratigraphy) , computation , algorithm , statistics , paleontology , biology
The space time bilinear (STBL) model is a special form of a multiple bilinear time series that can be used to model time series which exhibit bilinear behaviour on a spatial neighbourhood structure. The STBL model and its identification have been proposed and discussed by Dai and Billard (1998). The present work considers the problem of parameter estimation for the STBL model. A conditional maximum likelihood estimation procedure is provided through the use of a Newton–Raphson numerical optimization algorithm. The gradient vector and Hessian matrix are derived together with recursive equations for computation implementation. The methodology is illustrated with two simulated data sets, and one real‐life data set.