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时齐扩散过程的扩散系数跳跃有多大？AI 解读

We consider high-frequency observations from a one-dimensional time-homogeneous diffusion process Y . We assume that the diffusion coefficient $\sigma $ is continuously differentiable in y , but with a jump discontinuity at some level y , say $y=0$ . We first study sign-constrained kernel estimators of functions of the left and right limits of $\sigma $ at $0$ . These functions intricately depend on both limits. We propose a method to extricate these functions by searching…

极值极限簇大小分布的推断AI 解读

Any limiting point process for the time normalized exceedances of high levels by a stationary sequence is necessarily compound Poisson under appropriate long range dependence conditions. Typically exceedances appear in clusters. The underlying Poisson points represent the cluster positions and the multiplicities correspond to the cluster sizes. In the present paper we introduce estimators of the limiting cluster size probabilities, which are constructed through a recursive…

随机单位根模型AI 解读

This paper develops a dynamic switching model, with a random walk and a stationary regime, where the time spent in the random walk regime is endogeneously predetermined. More precisely, we assume that the process is recursively defined by Y t = μ + Y t −1 + ε t , with stochastic probability π rw ( Y t −1 ), Y t = μ + ε t , with stochastic probability 1 − π rw ( Y t −1 ), where (ε t ) is a strong white noise and π rw is a nondecreasing function. Then, the dynamics of the…