Online Drift Estimation for Jump-Diffusion Processes
46 Pages Posted: 10 Mar 2020 Last revised: 5 Feb 2021
Date Written: February 18, 2020
We show the convergence of an online stochastic gradient descent estimator to obtain the drift parameter of a continuous-time jump-diffusion process. The stochastic gradient descent follows a stochastic path in the gradient direction of a function to find a minimum, which in our case determines the estimate of the unknown drift parameter. We decompose the deviation of the stochastic descent direction from the deterministic descent direction into four terms: the weak solution of the non-local Poisson equation, a Riemann integral, a stochastic integral, and a covariation term. This decomposition is employed to prove the convergence of the online estimator and we use simulations to illustrate the performance of the online estimator.
Keywords: SGDCT, online estimation, jump-diffusion, extended Ito lemma, non-local Poisson equation, Levy process
JEL Classification: C1, C13, C15, C22
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