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.

在库存和航班价格中，时间序列的扩散和跳跃决定了价格随时间的演变。提出了一种跳扩散二进微粒滤波器，用于价格预测。在股票价格预测中，二分法包括对每个股票建模的潜在向量和对同一类别的公司集团进行建模的潜在向量。在飞行价格预测中，二元组分别由出发潜矢量和到达潜矢量组成。引入粒子系数来编码扩散和跳跃。假设扩散过程是几何布朗运动，其动力学通过卡尔曼滤波器进行建模。后验分布的负对数似然率通过围绕先前观察到的漂移参数的泰勒展开近似。得出相对于先前观察到的漂移参数的负对数似然率的一阶和二阶导数的有效近似值。为了推断突然的价格跳跃，使用了可逆的跳跃马尔可夫链蒙特卡洛框架。实验证明，与最新技术相比，价格上涨和扩散推断机制可导致更准确的预测。性能提升被证明具有统计学意义。