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Testing for a unit root in noncausal autoregressive models

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  • Saikkonen, Pentti
  • Sandberg, Rickard

Abstract

This work develops likelihood-based unit root tests in the noncausal autoregressive (NCAR) model formulated by Lanne and Saikkonen (2011, Journal of Time Series Econometrics 3, Iss. 3, Article 2). The possible unit root is assumed to appear in the causal autoregressive polynomial and for reasons of identification the error term of the model is supposed to be non-Gaussian. In order to derive the tests, asymptotic properties of the maximum likelihood estimators are established under the unit root hypothesis. The limiting distributions of the proposed tests depend on a nuisance parameter determined by the distribution of the error term of the model. A simple procedure to handle this nuisance parameter dependence in applications is proposed. Finite sample properties of the tests are examined by means of Monte Carlo simulations. The results show that the size properties of the tests are satisfactory and the power against stationary NCAR alternatives is significantly higher than the power of conventional Dickey-Fuller tests and the M-tests of Lucas (1995, Econometric Theory 11, 331-346). In an empirical application to a Finnish interest rate series evidence in favour of a stationary NCAR model with leptokurtic errors is found.

Suggested Citation

  • Saikkonen, Pentti & Sandberg, Rickard, 2013. "Testing for a unit root in noncausal autoregressive models," Bank of Finland Research Discussion Papers 26/2013, Bank of Finland.
    • Handle: RePEc:zbw:bofrdp:rdp2013_026
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    Cited by:

    1. Frédérique Bec & Heino Bohn Nielsen & Sarra Saïdi, 2020. "Mixed Causal–Noncausal Autoregressions: Bimodality Issues in Estimation and Unit Root Testing," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 82(6), pages 1413-1428, December.
    2. Frédérique Bec & Alain Guay & Heino Bohn Nielsen & Sarra Saïdi, 2022. "Power of unit root tests against nonlinear and noncausal alternatives," THEMA Working Papers 2022-14, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
    3. Anders Rygh Swensen, 2022. "On causal and non‐causal cointegrated vector autoregressive time series," Journal of Time Series Analysis, Wiley Blackwell, vol. 43(2), pages 178-196, March.
    4. Jean-Baptiste MICHAU, 2019. "Helicopter Drops of Money under Secular Stagnation," Working Papers 2019-10, Center for Research in Economics and Statistics.
    5. Alain Hecq & Sean Telg & Lenard Lieb, 2017. "Do Seasonal Adjustments Induce Noncausal Dynamics in Inflation Rates?," Econometrics, MDPI, vol. 5(4), pages 1-22, October.
    6. Christian Gouriéroux & Yang Lu, 2023. "Noncausal affine processes with applications to derivative pricing," Mathematical Finance, Wiley Blackwell, vol. 33(3), pages 766-796, July.

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