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Estimation in nonstationary random coefficient autoregressive models
Author(s) -
Berkes István,
Horváth Lajos,
Ling Shiqing
Publication year - 2009
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.1467-9892.2009.00615.x
Subject(s) - mathematics , autoregressive model , estimator , maximum likelihood , statistics , unit root , asymptotic distribution , star model , estimation theory , autoregressive integrated moving average , time series
. We investigate the estimation of parameters in the random coefficient autoregressive (RCA) model X k = ( ϕ + b k ) X k −1 + e k , where ( ϕ , ω 2 , σ 2 ) is the parameter of the process, , . We consider a nonstationary RCA process satisfying E log | ϕ + b 0 | ≥ 0 and show that σ 2 cannot be estimated by the quasi‐maximum likelihood method. The asymptotic normality of the quasi‐maximum likelihood estimator for ( ϕ , ω 2 ) is proven so that the unit root problem does not exist in the RCA model.