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Weak identification in the ESTAR model and a new model
Author(s) -
Heinen Florian,
Michael Stefanie,
Sibbertsen Philipp
Publication year - 2013
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/jtsa.12008
Subject(s) - mathematics , autoregressive model , identification (biology) , estimator , parameter identification problem , variance (accounting) , econometrics , exponential function , unit root , term (time) , mathematical optimization , statistics , model parameter , mathematical analysis , botany , accounting , business , biology , physics , quantum mechanics
Determining good parameter estimates in (exponential smooth transition autoregressive) models is known to be difficult. We show that the phenomena of getting strongly biased estimators is a consequence of the so‐called identification problem, the problem of properly distinguishing the transition function in relation to extreme parameter combinations. This happens in particular for either very small or very large values of the error term variance. Furthermore, we introduce a new alternative model – the TSTAR model – which has similar properties as the ESTAR model but reduces the effects of the identification problem. We also derive a linearity and a unit root test for this model.