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基于计数数据的 Hawkes 过程谱估计AI 解读

This paper presents a parametric estimation method for ill-observed linear stationary Hawkes processes. When the exact locations of points are not observed, but only counts over time intervals of fixed size, methods based on the likelihood are not feasible. We show that spectral estimation based on Whittle’s method is adapted to this case and provides consistent and asymptotically normal estimators, provided a mild moment condition on the reproduction function. Simulated…

存在平滑非参数趋势时的长记忆估计AI 解读

We consider semiparametric estimation of the long-memory parameter of a stationary process in the presence of an additive nonparametric mean function. We use a semiparametric Whittle-type estimator, applied to the tapered, differenced series. Because the mean function is not necessarily a polynomial of finite order, no amount of differencing will completely remove the mean. We establish a central limit theorem for the estimator of the memory parameter, assuming that a slowly…