Comparing statistical and deep learning techniques for parameter estimation of continuous-time stochastic differentiable equations

TL;DR

This paper compares traditional statistical methods and modern deep learning models, specifically RNNs, for estimating parameters of stochastic differential equations like the Ornstein-Uhlenbeck process, focusing on accuracy and computational efficiency.

Contribution

It provides an empirical comparison between MLE and RNN approaches for parameter estimation in stochastic differential equations.

Findings

RNNs can achieve comparable or better estimation accuracy than MLE.

Deep learning methods may offer computational advantages in certain scenarios.

The study highlights the potential of neural networks for stochastic process modeling.

Abstract

Stochastic differential equations such as the Ornstein-Uhlenbeck process have long been used to model realworld probablistic events such as stock prices and temperature fluctuations. While statistical methods such as Maximum Likelihood Estimation (MLE), Kalman Filtering, Inverse Variable Method, and more have historically been used to estimate the parameters of stochastic differential equations, the recent explosion of deep learning technology suggests that models such as a Recurrent Neural Network (RNN) could produce more precise estimators. We present a series of experiments that compare the estimation accuracy and computational expensiveness of a statistical method (MLE) with a deep learning model (RNN) for the parameters of the Ornstein-Uhlenbeck process.