A Practical Inference for Discretely Observed Jump-diffusions from Finite Samples
نویسندگان
چکیده
In the inference for jump-diffusion processes, we often need to get the information of the jump part and of the continuous part separately from the data. Although some asymptotic theories have been studied on this issue, a practical interest is the inference from finitely many discrete samples. In this paper we propose a numerical procedure to construct a filter to judge whether or not a jump occurred from finite samples. The paper includes a discussion about the validity of the procedure.
منابع مشابه
Consistency of Bayesian nonparametric inference for discretely observed jump diffusions
We introduce verifiable criteria for weak posterior consistency of Bayesian nonparametric inference for jump diffusions with unit diffusion coefficient in arbitrary dimension. The criteria are expressed in terms of coefficients of the SDEs describing the process, and do not depend on intractable quantities such as transition densities. In particular, we are able to show that posterior consisten...
متن کاملEstimation in discretely observed diffusions killed at a threshold
Parameter estimation in diffusion processes from discrete observations up to a first-hitting time is clearly of practical relevance, but does not seem to have been studied so far. In neuroscience, many models for the membrane potential evolution involve the presence of an upper threshold. Data are modeled as discretely observed diffusions which are killed when the threshold is reached. Statisti...
متن کاملStatistical inference for discretely observed Markov jump processes
Likelihood inference for discretely observed Markov jump processes with finite state space is investigated. The existence and uniqueness of the maximum likelihood estimator of the intensity matrix are investigated. This topic is closely related to the imbedding problem for Markov chains. It is demonstrated that the maximum likelihood estimator can be found either by the EM algorithm or by a Mar...
متن کاملExact and computationally efficient likelihood–based estimation for discretely observed diffusion processes
The objective of this paper is to present a novel methodology for likelihood-based inference for discretely observed diffusions. We propose Monte Carlo methods, which build on recent advances on the exact simulation of diffusions, for performing maximum likelihood and Bayesian estimation.
متن کاملNonparametric Transition-Based Tests for Jump Diffusions
We develop a specification test for the transition density of a discretely sampled continuous-time jump-diffusion process, based on a comparison of a nonparametric estimate of the transition density or distribution function with their corresponding parametric counterparts assumed by the null hypothesis. As a special case, our method applies to pure diffusions. We provide a direct comparison of ...
متن کامل