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Computationally efficient bootstrap prediction intervals for returns and volatilities in ARCH and GARCH processes
Author(s) -
Chen Bei,
Gel Yulia R.,
Balakrish.,
Abraham Bovas
Publication year - 2011
Publication title -
journal of forecasting
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.543
H-Index - 59
eISSN - 1099-131X
pISSN - 0277-6693
DOI - 10.1002/for.1197
Subject(s) - autoregressive conditional heteroskedasticity , arch , econometrics , sampling (signal processing) , prediction interval , volatility (finance) , computer science , representation (politics) , nonlinear system , statistics , mathematics , engineering , civil engineering , physics , filter (signal processing) , quantum mechanics , politics , law , computer vision , political science
We propose a novel, simple, efficient and distribution‐free re‐sampling technique for developing prediction intervals for returns and volatilities following ARCH/GARCH models. In particular, our key idea is to employ a Box–Jenkins linear representation of an ARCH/GARCH equation and then to adapt a sieve bootstrap procedure to the nonlinear GARCH framework. Our simulation studies indicate that the new re‐sampling method provides sharp and well calibrated prediction intervals for both returns and volatilities while reducing computational costs by up to 100 times, compared to other available re‐sampling techniques for ARCH/GARCH models. The proposed procedure is illustrated by an application to Yen/U.S. dollar daily exchange rate data. Copyright © 2010 John Wiley & Sons, Ltd.