TY - JOUR
T1 - To infinity and beyond
T2 - Efficient computation of ARCH(infinity) models
AU - Nielsen, Morten Orregaard
AU - Noel, Antoine L.
PY - 2021/5
Y1 - 2021/5
N2 - 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.
AB - 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.
KW - Circular convolution theorem
KW - conditional heteroskedasticity
KW - fast Fourier transform
KW - FIGARCH
KW - truncation
KW - LONG-MEMORY
KW - CONDITIONAL HETEROSCEDASTICITY
UR - http://www.scopus.com/inward/record.url?scp=85097820336&partnerID=8YFLogxK
U2 - 10.1111/jtsa.12570
DO - 10.1111/jtsa.12570
M3 - Journal article
SN - 0143-9782
VL - 42
SP - 338
EP - 354
JO - Journal of Time Series Analysis
JF - Journal of Time Series Analysis
IS - 3
ER -