Analytical Derivates of the APARCH Model

Sébastien Laurent

Computational Economics, 2004, vol. 24, issue 1, 57 pages

Abstract: This paper derives analytical expressions for the score of the APARCH model of Ding et al. (1993). Interestingly, doing so we derive the analytical score of a broad range of GARCH model since the APARCH model nests at least seven specifications. The use of the APARCH model is now widespread in the literature. However, all the existing applications rely on numerical techniques to calculate the gradients. The paper shows that analytical gradients highly speed-up maximum-likelihood estimation.

Date: 2004
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