To infinity and beyond: Efficient computation of ARCH(\infty) models

Arbeitspapier

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.

Object Details

• Language: Englisch

References and Relationships

• Bibliographic citation: Series: Queen’s Economics Department Working Paper ; No. 1425

Classification and Topics

• Classification: Wirtschaft ; Single Equation Models; Single Variables: Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes ; Financial Econometrics ; Computational Techniques; Simulation Modeling ; Econometric Software
• Subject: Circular convolution theorem ; conditional heteroskedasticity ; fast Fouriertransform ; FIGARCH ; truncation

Contributors, Places and Time

• Event: Geistige Schöpfung
• (who): Nielsen, Morten Ørregaard ; Noël, Antoine
• Event: Veröffentlichung
• (who): Queen's University, Department of Economics
• (where): Kingston (Ontario)
• (when): 2020

Further information

• Handle: http://hdl.handle.net/10419/230578
• Last update: 10.03.2025, 11:46 AM CET