Optimal Estimation of Generic Dynamics by Path-Dependent Neural Jump ODEs
This work addresses forecasting challenges for irregularly observed time series in fields like finance, though it is incremental as it builds on an existing framework.
This paper tackles the problem of forecasting general stochastic processes, including non-Markovian or discontinuous ones with incomplete observations, by extending the Neural Jump ODE framework; it shows that the path-dependent version outperforms the original in non-Markovian cases and applies successfully to stochastic filtering and limit order book data.
This paper studies the problem of forecasting general stochastic processes using a path-dependent extension of the Neural Jump ODE (NJ-ODE) framework \citep{herrera2021neural}. While NJ-ODE was the first framework to establish convergence guarantees for the prediction of irregularly observed time series, these results were limited to data stemming from Itô-diffusions with complete observations, in particular Markov processes, where all coordinates are observed simultaneously. In this work, we generalise these results to generic, possibly non-Markovian or discontinuous, stochastic processes with incomplete observations, by utilising the reconstruction properties of the signature transform. These theoretical results are supported by empirical studies, where it is shown that the path-dependent NJ-ODE outperforms the original NJ-ODE framework in the case of non-Markovian data. Moreover, we show that PD-NJ-ODE can be applied successfully to classical stochastic filtering problems and to limit order book (LOB) data.