A Hawkes model with CARMA(p,q) intensity
提出一种CARMA(p,q)-Hawkes模型，其强度服从连续时间自回归移动平均过程，以克服传统霍克斯模型自相关函数单调递减的局限，并研究了平稳性、正性和强混合性质，给出了基于似然和自相关函数的估计案例。
In this paper we introduce a new model, named CARMA(p,q)-Hawkes, as the Hawkes model with exponential kernel implies a strictly decreasing behaviour of the autocorrelation function while empirical evidences reject its monotonicity. The proposed model is a Hawkes process where the intensity follows a Continuous Time Autoregressive Moving Average (CARMA) process. We also study the conditions for the stationarity and the positivity of the intensity and the strong mixing property for the increments. Furthermore, we present two estimation case studies based respectively on the likelihood and on the autocorrelation function.