Estimation in nonstationary random coefficient autoregressive models
AbstractWe investigate the estimation of parameters in the random coefficient autoregressive (RCA) model X_k = (ϕ + b_k)X_k - 1 + e_k, where (ϕ, omega-super-2, σ-super-2) is the parameter of the process, , . We consider a nonstationary RCA process satisfying E log |ϕ + b_0| >= 0 and show that σ-super-2 cannot be estimated by the quasi-maximum likelihood method. The asymptotic normality of the quasi-maximum likelihood estimator for (ϕ, omega-super-2) is proven so that the unit root problem does not exist in the RCA model. Copyright 2009 Blackwell Publishing Ltd
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Bibliographic InfoArticle provided by Wiley Blackwell in its journal Journal of Time Series Analysis.
Volume (Year): 30 (2009)
Issue (Month): 4 (07)
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Web page: http://www.blackwellpublishing.com/journal.asp?ref=0143-9782
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- Nagakura, Daisuke, 2009. "Asymptotic theory for explosive random coefficient autoregressive models and inconsistency of a unit root test against a stochastic unit root process," Statistics & Probability Letters, Elsevier, Elsevier, vol. 79(24), pages 2476-2483, December.
- Aknouche, Abdelhakim & Al-Eid, Eid M. & Hmeid, Aboubakry M., 2011. "Offline and online weighted least squares estimation of nonstationary power ARCH processes," Statistics & Probability Letters, Elsevier, Elsevier, vol. 81(10), pages 1535-1540, October.
- Daisuke Nagakura, 2009. "Inconsistency of a Unit Root Test against Stochastic Unit Root Processes," IMES Discussion Paper Series 09-E-23, Institute for Monetary and Economic Studies, Bank of Japan.
- Abdelhakim Aknouche & Eid Al-Eid, 2012. "Asymptotic inference of unstable periodic ARCH processes," Statistical Inference for Stochastic Processes, Springer, Springer, vol. 15(1), pages 61-79, April.
- Abdelhakim Aknouche, 2012. "Multistage weighted least squares estimation of ARCH processes in the stable and unstable cases," Statistical Inference for Stochastic Processes, Springer, Springer, vol. 15(3), pages 241-256, October.
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