Abstract
In this paper, we propose a new bootstrap algorithm to obtain prediction intervals for generalized autoregressive conditionally heteroscedastic (GARCH(1,1)) process which can be applied to construct prediction intervals for future returns and volatilities. The advantages of the proposed method are twofold: it (a) often exhibits improved performance and (b) is computationally more efficient compared to other available resampling methods. The superiority of this method over the other resampling method-based prediction intervals is explained with Spearman’s rank correlation coefficient. The finite sample properties of the proposed method are also illustrated by an extensive simulation study and a real-world example.
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Acknowledgements
We thank two anonymous referees for careful reading of the paper and valuable suggestions and comments, which have helped us produce a significantly better paper. We are also grateful to the Editor for offering the opportunity to publish our work. Beste and Ufuk Beyaztas gratefully acknowledge the support from Department of Mathematics, Lehigh University, where major part of this work was done while they were visiting there in 2015–2016. Ufuk Beyaztas was supported by a grant from the Scientific and Technological Research Council of Turkey (TUBITAK) grant no: 1059B141500288. Soutir Bandyopadhyay’s work has been partially supported by NSF-DMS 1406622.
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Beyaztas, B.H., Beyaztas, U., Bandyopadhyay, S. et al. New and Fast Block Bootstrap-Based Prediction Intervals for GARCH(1,1) Process with Application to Exchange Rates. Sankhya A 80, 168–194 (2018). https://doi.org/10.1007/s13171-017-0098-2
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DOI: https://doi.org/10.1007/s13171-017-0098-2