Motivated by estimating the lead-lag relationships in high-frequency financial data, we propose noisy bivariate Neyman-Scott point processes with gamma kernels (NBNSP-G). NBNSP-G tolerates noises that are not necessarily Poissonian and has an intuitive interpretation. Our experiments suggest that NBNSP-G can explain the correlation of orders of two stocks well. A composite-type quasi-likelihood is employed to estimate the parameters of the model. However, when one tries to prove consistency and asymptotic normality, NBNSP-G breaks the boundedness assumption on the moment density functions commonly assumed in the literature. Therefore, under more relaxed conditions, we show consistency and asymptotic normality for bivariate point process models, which include NBNSP-G. Our numerical simulations also show that the estimator is indeed likely to converge.

翻译：受高频金融数据中领先-滞后关系估计问题的启发，本文提出采用伽马核的含噪二元Neyman-Scott点过程模型（NBNSP-G）。该模型能够容纳非泊松分布的噪声，且具有直观的解释意义。实验表明NBNSP-G能较好地解释两只股票订单间的相关性。我们采用复合型拟似然方法对模型参数进行估计。然而，在尝试证明估计量的一致性与渐近正态性时，NBNSP-G突破了现有文献中普遍设定的矩密度函数有界性假设。为此，我们在更宽松的条件下证明了包含NBNSP-G在内的二元点过程模型参数估计量的一致性与渐近正态性。数值模拟结果也表明该估计量确实具有收敛性。