 To infinity and beyond: Efficient computation of ARCH(∞) modelsMorten Nielsen and Antoine Noël Journal of Time Series Analysis, 2021, vol. 42, issue 3, 338-354 Abstract: This article provides an exact algorithm for efficient computation of the time series of conditional variances, and hence the likelihood function, of models that have an ARCH(∞) representation. This class of models includes, for example, the fractionally integrated generalized autoregressive conditional heteroskedasticity (FIGARCH) model. Our algorithm is a variation of the fast fractional difference algorithm of Jensen, A.N. and M.Ø. Nielsen (2014), Journal of Time Series Analysis 35, 428–436. It takes advantage of the fast Fourier transform (FFT) to achieve an order of magnitude improvement in computational speed. The efficiency of the algorithm allows estimation (and simulation/bootstrapping) of ARCH(∞) models, even with very large data sets and without the truncation of the filter commonly applied in the literature. In Monte Carlo simulations, we show that the elimination of the truncation of the filter reduces the bias of the quasi‐maximum‐likelihood estimators and improves out‐of‐sample forecasting. Our results are illustrated in two empirical examples. Date: 2021 Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:bla:jtsera:v:42:y:2021:i:3:p:338-354 Ordering information: This journal article can be ordered from Access Statistics for this article Journal of Time Series Analysis is currently edited by M.B. Priestley More articles in Journal of Time Series Analysis from Wiley Blackwell |
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