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On an independent and identically distributed mixture bilinear time‐series model
Author(s) -
Aknouche Abdelhakim,
Rabehi Nadia
Publication year - 2010
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.1467-9892.2009.00649.x
Subject(s) - mathematics , bilinear interpolation , ergodicity , series (stratigraphy) , diagonal , covariance , independent and identically distributed random variables , conditional independence , conditional probability distribution , nonlinear system , representation (politics) , autoregressive model , random variable , statistics , law , paleontology , physics , geometry , quantum mechanics , politics , political science , biology
A class of nonlinear time‐series models in which the underlying process follows a finite mixture of bilinear representations is proposed. The mixture feature appears in the conditional distribution of the process which is given as a finite mixture of distributions evaluated at the normed innovations of diagonal bilinear specifications. This class is aimed at capturing special characteristics exhibited by many observed time series such as tail heaviness, multimodality, asymmetry and change in regime. Some probabilistic properties of the proposed model, namely strict and second‐order stationarity, geometric ergodicity, covariance structure, existence of higher order moments, tail behaviour and invertibility, are first studied. Parameter estimation is then performed through the EM algorithm, performance of which is shown via simulation experiments. Applications to some real‐time‐series data are proposed and through which it is shown how neglecting the mixture framework in a bilinear representation results in a loss in adequacy.