Please use this identifier to cite or link to this item: http://hdl.handle.net/10419/230578
Authors: 
Nielsen, Morten Ørregaard
Noël, Antoine
Year of Publication: 
2020
Series/Report no.: 
Queen’s Economics Department Working Paper No. 1425
Abstract: 
This paper 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(É) representation. This class of models includes, e.g., the fractionally integrated generalized autoregressive conditional heteroskedasticity (FIGARCH) model. Our algorithm is a variation of the fast fractional difference algorithm of Jensen and Nielsen (2014). 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(É) models, even with very large data sets and without the truncation of the filter commonly applied in the literature. We also show that the elimination of the truncation of the filter substantially reduces the bias of the quasi-maximum-likelihood estimators. Our results are illustrated in two empirical examples.
Subjects: 
Circular convolution theorem
conditional heteroskedasticity
fast Fouriertransform
FIGARCH
truncation
JEL: 
C22
C58
C63
C87
Document Type: 
Working Paper

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