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Unit root testing in the presence of ARFIMA–GARCH errors

Authors

  • Gaowen Wang

    Corresponding author
    1. Department of Banking and Finance, Takming University of Science and Technology, No. 56, Sec. l, Huanshan Rd., Neihu, Taipei 11451, Taiwan
    • Department of Banking and Finance, Takming University of Science and Technology, No. 56, Sec. l, Huanshan Rd., Neihu, Taipei 11451, Taiwan
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Abstract

We consider asymptotic behavior of self-normalized sums of autoregressive fractionally integrated moving average (ARFIMA) processes whose innovations are GARCH errors. The asymptotic distribution of the sums is derived under very mild conditions. Applications to unit root tests with ARFIMA–GARCH errors are discussed. It is shown that even when the errors exhibit both long-range dependence and heavy-tailed conditional heteroscedasticity, the asymptotic distributions of the Dickey–Fuller ρ-type tests are functionals of standard Brownian motion rather than those of fractional Brownian motions. Some Monte Carlo simulations are provided to illustrate the finite sample properties of two of the tests. Copyright © 2010 John Wiley & Sons, Ltd.

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