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Identifying Price Jumps from Daily Data with Bayesian vs. Non-Parametric Methods, Milan Fičura, Jiří Witzany, 2017

Identifying Price Jumps from Daily Data with Bayesian vs. Non-Parametric Methods, Milan Fičura, Jiří Witzany, 2017

Asset price jumps, Bayesian estimation, Hawkes process, L-Estimator, MCMC, Particle filters, power variation estimators, self-exciting jumps, SVJD

Non-parametric approach to financial time series jump estimation, using the L-Estimator, is compared with the parametric approach utilizing a Stochastic-Volatility-Jump-Diffusion (SVJD) model, estimated with MCMC and extended with Particle Filters to estimate the out-sample evolution of its latent state variables, such as the jump occurrences. The comparison is performed on simulated time series with different kinds of dynamics, including Poisson jumps, self-exciting Hawkes jumps with long-term clustering, as well as co-jumps. In addition to that, a comparison is performed on the real world daily time series of 4 major currency exchange rates. The results from the simulation study show that for the purposes of in-sample estimation does the MCMC based parametric approach significantly outperform the L-Estimator. In the case of the out-sample estimates, based on a combination of MCMC an Particle Filters, used to sequentially estimate the jump occurrences immediately at the times at which the jumps occur, does the parametric approach achieve a similar accuracy as the non-parametric one in the case of the simulations with Poisson jumps that are relatively large, and it outperforms the non-parametric approach in the case of Hawkes jumps when the jumps are large. On the other hand, the L-Estimator provides better results than the parametric approach in all of the cases when the simulated jumps are small (1% or less), regardless of the jump process dynamics. The application of the methods to foreign exchange rate time series further shows that the estimates of the parametric method may be biased in the case when large outlier jumps occur in the time series as well as when the stochastic volatility grows too high (as happened during the crisis). In both of these cases, the non-parametric L-Estimator based approach seems to provide more robust jump estimates, less influenced by the mentioned issues.