Maximum likelihood estimation of diffusions by continuous time Markov chain
نویسندگان
چکیده
A novel method is presented for estimating the parameters of a parametric diffusion process. The approach based on closed-form Maximum Likelihood estimator an approximating Continuous Time Markov Chain (CTMC) Unlike typical time discretization approaches, such as pseudo-likelihood approximations with Shoji-Ozaki or Kessler's method, CTMC approximation introduces no time-discretization error during parameter estimation, and thus well-suited econometric situations infrequently sampled data. Due to structure CTMC, are obtained sample likelihood which hold general univariate diffusions. Comparisons state-discretization approximate MLE (time-discretization) Exact (when applicable) demonstrate favorable performance estimator. Simulated examples provided in addition real data experiments FX rates constant maturity interest rates.
منابع مشابه
Quasi-Maximum Likelihood Estimation of Multivariate Diffusions
This paper introduces quasi-maximum likelihood estimator for multivariate diffusions based on discrete observations. A numerical solution to the stochastic differential equation is obtained by higher order Wagner-Platen approximation and it is used to derive the first two conditional moments. Monte Carlo simulation shows that the proposed method has good finite sample property for both normal a...
متن کاملMaximum Likelihood Drift Estimation for Multiscale Diffusions
We study the problem of parameter estimation using maximum likelihood for fast/slow systems of stochastic differential equations. Our aim is to shed light on the problem of model/data mismatch at small scales. We consider two classes of fast/slow problems for which a closed coarse-grained equation for the slow variables can be rigorously derived, which we refer to as averaging and homogenizatio...
متن کاملEfficient maximum likelihood parameterization of continuous-time Markov processes.
Continuous-time Markov processes over finite state-spaces are widely used to model dynamical processes in many fields of natural and social science. Here, we introduce a maximum likelihood estimator for constructing such models from data observed at a finite time interval. This estimator is dramatically more efficient than prior approaches, enables the calculation of deterministic confidence in...
متن کاملEfficient Continuous-Time Markov Chain Estimation
Many problems of practical interest rely on Continuous-time Markov chains (CTMCs) defined over combinatorial state spaces, rendering the computation of transition probabilities, and hence probabilistic inference, difficult or impossible with existing methods. For problems with countably infinite states, where classical methods such as matrix exponentiation are not applicable, the main alternati...
متن کاملMaximum likelihood trajectories for continuous-time Markov chains
Continuous-time Markov chains are used to model systems in which transitions between states as well as the time the system spends in each state are random. Many computational problems related to such chains have been solved, including determining state distributions as a function of time, parameter estimation, and control. However, the problem of inferring most likely trajectories, where a traj...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Computational Statistics & Data Analysis
سال: 2022
ISSN: ['0167-9473', '1872-7352']
DOI: https://doi.org/10.1016/j.csda.2021.107408