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Double AR model without intercept: An alternative to modeling nonstationarity and heteroscedasticity

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  • Dong Li
  • Shaojun Guo
  • Ke Zhu

Abstract

This paper presents a double AR model without intercept (DARWIN model) and provides us a new way to study the nonstationary heteroscedastic time series. It is shown that the DARWIN model is always nonstationary and heteroscedastic, and its sample properties depend on the Lyapunov exponent. An easy-to-implement estimator is proposed for the Lyapunov exponent, and it is unbiased, strongly consistent, and asymptotically normal. Based on this estimator, a powerful test is constructed for testing the ordinary oscillation of the model. Moreover, this paper proposes the quasi-maximum likelihood estimator (QMLE) for the DARWIN model, which has an explicit form. The strong consistency and asymptotic normality of the QMLE are established regardless of the sign of the Lyapunov exponent. Simulation studies are conducted to assess the performance of the estimation and testing, and an empirical example is given for illustrating the usefulness of the DARWIN model.

Suggested Citation

  • Dong Li & Shaojun Guo & Ke Zhu, 2019. "Double AR model without intercept: An alternative to modeling nonstationarity and heteroscedasticity," Econometric Reviews, Taylor & Francis Journals, vol. 38(3), pages 319-331, March.
    • Handle: RePEc:taf:emetrv:v:38:y:2019:i:3:p:319-331
    DOI: 10.1080/07474938.2017.1310080
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    Cited by:

    1. Djogbenou, Antoine & Inan, Emre & Jasiak, Joann, 2023. "Time-varying coefficient DAR model and stability measures for stablecoin prices: An application to Tether," Journal of International Money and Finance, Elsevier, vol. 139(C).
    2. Li, Dong & Tao, Yuxin & Yang, Yaxing & Zhang, Rongmao, 2023. "Maximum likelihood estimation for α-stable double autoregressive models," Journal of Econometrics, Elsevier, vol. 236(1).

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