A jump-diffusion particle filter for price prediction

Abstract

In stock and flight price time series diffusion and jumps govern price evolution over time. A jump-diffusion dyadic particle filter is proposed for price prediction. In stock price prediction, the dyad comprises a latent vector modeling each stock and a latent vector modeling the group of companies in the same category. In flight price prediction, the dyad consists of a departure latent vector and an arrival latent vector, respectively. A particle coefficient is introduced to encode both diffusion and jumps. The diffusion process is assumed to be a geometric Brownian motion whose dynamics are modeled by a Kalman filter. The negative log-likelihood of the posterior distribution is approximated by a Taylor expansion around the previously observed drift parameter. Efficient approximations of the first and second-order derivatives of the negative log-likelihood with respect to the previously observed drift parameter are derived. To infer sudden price jumps, a reversible jump Markov chain Monte-Carlo framework is used. Experiments have demonstrated that price jump and diffusion inference mechanisms lead to more accurate predictions compared to state-of-the-art techniques. Performance gains are attested to be statistically significant.