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Testing the Null Hypothesis of Nonstationary Long Memory Against the Alternative Hypothesis of a Nonlinear Ergodic Model

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  • George Kapetanios
  • Yongcheol Shin

Abstract

Interest in the interface of nonstationarity and nonlinearity has been increasing in the econometric literature. This paper provides a formal method of testing for nonstationary long memory against the alternative of a particular form of nonlinear ergodic processes; namely, exponential smooth transition autoregressive processes. In this regard, the current paper provides a significant generalization to existing unit root tests by allowing the null hypothesis to encompass a much larger class of nonstationary processes. The asymptotic theory associated with the proposed Wald statistic is derived, and Monte Carlo simulation results confirm that the Wald statistics have reasonably correct size and good power in small samples. In an application to real interest rates and the Yen real exchange rates, we find that the tests are able to distinguish between these competing processes in most cases, supporting the long-run Purchasing Power Parity (PPP) and Fisher hypotheses. But, there are a few cases in which long memory and nonlinear ergodic processes display similar characteristics and are thus confused with each other in small samples.

Suggested Citation

  • George Kapetanios & Yongcheol Shin, 2011. "Testing the Null Hypothesis of Nonstationary Long Memory Against the Alternative Hypothesis of a Nonlinear Ergodic Model," Econometric Reviews, Taylor & Francis Journals, vol. 30(6), pages 620-645.
    • Handle: RePEc:taf:emetrv:v:30:y:2011:i:6:p:620-645
    DOI: 10.1080/07474938.2011.553568
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    References listed on IDEAS

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    1. Kapetanios, G. & Weeks, M., 2003. "Non-nested Models and the likelihood Ratio Statistic: A Comparison of Simulation and Bootstrap-based Tests," Cambridge Working Papers in Economics 0308, Faculty of Economics, University of Cambridge.
    2. repec:cdl:ucsdec:qt4d60t4jh is not listed on IDEAS
    3. George Kapetanios & Yongcheol Shin, 2003. "Testing for Nonstationary Long Memory against Nonlinear Ergodic Models," Working Papers 500, Queen Mary University of London, School of Economics and Finance.
    4. Joon Y. Park & Mototsugu Shintani, 2005. "Testing for a Unit Root against Transitional Autoregressive Models," Vanderbilt University Department of Economics Working Papers 05010, Vanderbilt University Department of Economics.
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    3. Geoffrey Poitras & John Heaney, 2015. "Classical Ergodicity and Modern Portfolio Theory," Post-Print hal-03680380, HAL.
    4. Gil-Alana, Luis A. & Gupta, Rangan & Shittu, Olanrewaju I. & Yaya, OlaOluwa S., 2018. "Market efficiency of Baltic stock markets: A fractional integration approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 511(C), pages 251-262.
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    7. Poitras, Geoffrey, 2018. "The pre-history of econophysics and the history of economics: Boltzmann versus the marginalists," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 507(C), pages 89-98.

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