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Estimation and testing stationarity for double-autoregressive models

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  • Shiqing Ling

Abstract

The paper considers the double-autoregressive model "y" "t"  = "φ""y" "t" - 1 +"ϵ" "t" with "ϵ" "t"  = . Consistency and asymptotic normality of the estimated parameters are proved under the condition "E" ln |"φ" +√"&agr;""η" "t" |>0, which includes the cases with |"φ"|=1 or |"φ"|>1 as well as . It is well known that all kinds of estimators of "φ" in these cases are not normal when "ϵ" "t" are independent and identically distributed. Our result is novel and surprising. Two tests are proposed for testing stationarity of the model and their asymptotic distributions are shown to be a function of bivariate Brownian motions. Critical values of the tests are tabulated and some simulation results are reported. An application to the US 90-day treasury bill rate series is given. Copyright 2004 Royal Statistical Society.

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Bibliographic Info

Article provided by Royal Statistical Society in its journal Journal of the Royal Statistical Society Series B.

Volume (Year): 66 (2004)
Issue (Month): 1 ()
Pages: 63-78

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Handle: RePEc:bla:jorssb:v:66:y:2004:i:1:p:63-78

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Cited by:
  1. Guo, Shaojun & Ling, Shiqing & Zhu, Ke, 2013. "Factor double autoregressive models with application to simultaneous causality testing," MPRA Paper 51570, University Library of Munich, Germany.
  2. Nikolay Gospodinov & Taisuke Otsu, 2008. "Local GMM Estimation of Time Series Models with Conditional Moment Restrictions," Working Papers 08010, Concordia University, Department of Economics.
  3. Wang, Gaowen, 2006. "A note on unit root tests with heavy-tailed GARCH errors," Statistics & Probability Letters, Elsevier, vol. 76(10), pages 1075-1079, May.
  4. Francq, Christian & Zakoian, Jean-Michel, 2012. "Risk-parameter estimation in volatility models," MPRA Paper 41713, University Library of Munich, Germany.
  5. Westerlund, Joakim & Larsson, Rolf, 2009. "Testing for a Unit Root in a Random Coefficient Panel Data Model," Working Papers in Economics 383, University of Gothenburg, Department of Economics.
  6. Rodrigues, Paulo M.M. & Rubia, Antonio, 2005. "The performance of unit root tests under level-dependent heteroskedasticity," Economics Letters, Elsevier, vol. 89(3), pages 262-268, December.
  7. Liu, Ji-Chun, 2012. "Structure of a double autoregressive process driven by a hidden Markov chain," Statistics & Probability Letters, Elsevier, vol. 82(7), pages 1468-1473.
  8. Christian Francq & Jean-Michel Zakoïan, 2013. "Optimal predictions of powers of conditionally heteroscedastic processes," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 75(2), pages 345-367, 03.
  9. Anthony J. Lawrance, 2010. "Volatile ARMA Modelling of GARCH Squares," Central European Journal of Economic Modelling and Econometrics, CEJEME, vol. 2(3), pages 195-203, June.
  10. Christian M. Dahl & Emma M. Iglesias, 2008. "The limiting properties of the QMLE in a general class of asymmetric volatility models," CREATES Research Papers 2008-38, School of Economics and Management, University of Aarhus.
  11. Bent Jesper Christensen & Christian M. Dahl & Emma M. Iglesias, 2008. "Semiparametric Inference in a GARCH-in-Mean Model," CREATES Research Papers 2008-46, School of Economics and Management, University of Aarhus.
  12. Westerlund, Joakim & Larsson, Rolf, 2012. "Testing for a unit root in a random coefficient panel data model," Journal of Econometrics, Elsevier, vol. 167(1), pages 254-273.
  13. Dong Li & Shiqing Ling & Jean-Michel Zakoian, 2013. "Asymptotic Inference in Multiple-Threshold Nonlinear Time Series Models," Working Papers 2013-51, Centre de Recherche en Economie et Statistique.
  14. Francq, Christian & Makarova, Svetlana & Zakoi[diaeresis]an, Jean-Michel, 2008. "A class of stochastic unit-root bilinear processes: Mixing properties and unit-root test," Journal of Econometrics, Elsevier, vol. 142(1), pages 312-326, January.
  15. Ling, Shiqing, 2007. "Self-weighted and local quasi-maximum likelihood estimators for ARMA-GARCH/IGARCH models," Journal of Econometrics, Elsevier, vol. 140(2), pages 849-873, October.

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