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Asymptotic Theory for a Stochastic Unit Root Model with Intercept and Under Mis-Specification of Intercept

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  • Lingjie Du

    (Zhejiang University)

  • Tianxiao Pang

    (Zhejiang University)

Abstract

Lieberman and Phillips (J Time Ser Anal 35(6):592–623 2014, J Econ 196(1):99–110 2017) proposed a stochastic unit root model, where the source of the variation of the autoregressive coefficient is driven by a stationary process. In this paper, we study a new stochastic unit root model, in which the source of the variation of the autoregressive coefficient is driven by a (nearly) non-stationary process. The asymptotic theory for this model is established not only in the presence of an intercept but also under a mis-specification of intercept. Our study reveals some new findings which are different from those established in Lieberman and Phillips (J Time Ser Anal 35(6):592–623 2014, J Econ 196(1):99–110 2017). Our theoretical results demonstrate that the statistical properties of the estimators of the model parameters vary from case to case, and depend not only on whether the parameters are zero or not, and the validity of the model specification, but also on the degree of the persistence of the source of the variation of the autoregressive coefficient. The application to a hypothesis testing with null hypothesis of a deterministic unit root model is briefly discussed. Monte Carlo simulations are conducted to examine the finite-sample performance for the estimators of model parameters. Our theoretical findings are supported by the simulation results.

Suggested Citation

  • Lingjie Du & Tianxiao Pang, 2021. "Asymptotic Theory for a Stochastic Unit Root Model with Intercept and Under Mis-Specification of Intercept," Methodology and Computing in Applied Probability, Springer, vol. 23(3), pages 767-799, September.
    • Handle: RePEc:spr:metcap:v:23:y:2021:i:3:d:10.1007_s11009-020-09781-2
    DOI: 10.1007/s11009-020-09781-2
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    References listed on IDEAS

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    1. Peter C. B. Phillips & Shuping Shi & Jun Yu, 2015. "Testing For Multiple Bubbles: Historical Episodes Of Exuberance And Collapse In The S&P 500," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 56(4), pages 1043-1078, November.
    2. Matei Demetrescu, 2010. "On the Dickey–Fuller test with White standard errors," Statistical Papers, Springer, vol. 51(1), pages 11-25, January.
    3. Peter C. B. Phillips & Yangru Wu & Jun Yu, 2011. "EXPLOSIVE BEHAVIOR IN THE 1990s NASDAQ: WHEN DID EXUBERANCE ESCALATE ASSET VALUES?," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 52(1), pages 201-226, February.
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