Abstract
In this paper we develop a bootstrap method for the construction of prediction intervals for an ARMA model when its innovations are an autoregressive conditional heteroscedastic process. We give a proof of the validity of the proposed bootstrap for this process. For this purpose we prove the convergence to zero in probability of the Mallows metric between the empirical distribution function and the theoretical distribution function of the residuals. The potential of the proposed method is assessed through a simulation study.
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This research was partially supported by Grant UZ-228-26 from the Spanish Ministry of Education and Grant UZ-228-25 from University of Zaragoza.
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Miguel, J.A., Olave, P. Bootstrapping forecast intervals in ARCH models. Test 8, 345–364 (1999). https://doi.org/10.1007/BF02595875
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DOI: https://doi.org/10.1007/BF02595875