Characterizing jumps using MEM and titration for chaotic patterns

made significant stride in clarifying the intimate relationship between two important latent processes, namely, volatility and jump diffusion. While various issues concerning volatility have been extensively investigated, the characterization of jumps is still in its infancy and can be interpreted under different perspectives. This includes qualitative study of news impact as reported by Barndorff-Nielsen & Shephard, central bank intervention on exchange rate (Beine et al, 2006), and quantitative analysis of jump statistics (Huang, 2004), amongst others. We consider two new perspectives in characterizing jumps. The first perspective focuses on the idea of conditional jump QV (Quadratic Variation) prediction, based on the framework of MEM (Multiplicative Error Model) (Engle & Gallo, 2006) with a non-negative input of realized jump QV (which is the difference between realized variance and multi-power variation). A comparison between conditional jump and realized jump is then made, by investigating the nonlinearities embedded in each process. Inspired by the work of titration for chaotic patterns (Poon and Barahona, 2001), our second perspective provides details on the nonlinearities associated with conditional and realized jump