Benchmarks and the accuracy of GARCH model estimation

Abstract

Reading's research outputs online 1 NOTICE: this is the author's version of a work that was accepted for publication in the International Journal of Forecasting. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in the International

Practical Issues in the Analysis of Univariate GARCH Models

“…As discussed in [69] and [20], there are several practical issues to consider in the maximization of (14). Starting values for the model parameters c, a i (i = 0, · · · , p) and b j (j = 1, · · · , q) need to be chosen and an initialization of 2 t and σ 2 t must be supplied.…”

“…EVIEWS, GAUSS, MATLAB, Ox, RATS, S-PLUS, TSP) and there are also a few free open source implementations. [41], [69], and [20] discussed numerical accuracy issues associated with maximizing the GARCH log-likelihood. They found that starting values, optimization algorithm choice, and use of analytic or numerical derivatives, and convergence criteria all influence the resulting numerical estimates of the GARCH parameters.…”

“…They found that starting values, optimization algorithm choice, and use of analytic or numerical derivatives, and convergence criteria all influence the resulting numerical estimates of the GARCH parameters. [69] and [20] studied estimation of a GARCH(1,1) model from a variety of commercial statistical packages using the exchange rate data of [15] as a benchmark. They found that it is often difficult to compare competing software since the exact construction of the GARCH likelihood is not always adequately described.…”

“…For example, a two components structure or ignored structural breaks in the unconditional variance ( [58] and [70]) can result in IGARCH behavior. Table 9 gives Lo's modified R/S statistic (20) applied to r 2 t and |r t | for Microsoft and the S&P 500. The 1% right tailed critical value for the test is 2.098 ( [62] Table 5.2) and so the modified R/S statistics are significant at the 1% level for both series providing evidence for long memory behavior in volatility.…”

Autoregressive Conditional Heteroscedasticity (ARCH) Models: A Review

“…Brooks et al [63] reviewed the most known software packages for estimation of ARCH models, and concluded that the estimation results differ considerably from one another. Table 2, in the Appendix, contains the ARCH models that have been presented in this section.…”