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Neural MJD: Neural Non-Stationary Merton Jump Diffusion for Time Series Prediction

NeurIPS 2025 · Time series › Causal and generative time series · approach: Diffusion models for time series · 0 citations (OpenAlex)

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Proposes Neural MJD, a neural parameterization of a non-stationary Merton jump diffusion whose time-varying SDE parameters are predicted by a network, trained with a truncated likelihood and forecast with an Euler-Maruyama-with-restart solver.

Problem

Time series forecasting with abrupt jumps and non-stationary dynamics, where deep black-box models lack explicit stochastic process structure and classical jump models assume stationarity and scale poorly.

Approach

Replace the constant parameters of Merton jump diffusion with time-inhomogeneous parameters predicted by a neural network conditioned on past data and context; train via a likelihood truncated at κ jumps per step, and simulate forecasts with an Euler-Maruyama solver that periodically resets to the analytic conditional mean.

Key results

• On S&P 500, Neural MJD reports MAE 15.4 and R^2 0.953 in mean metrics, versus 34.9 / 0.368 for flow matching (best baseline).
• On SafeGraph&Advan, Neural MJD achieves mean MAE 54.1 and R^2 0.549, slightly beating flow matching (54.5 / 0.540) on mean metrics and leading best-of-K metrics (minMAE 42.3 vs 47.8).
• Ablation on SafeGraph&Advan: replacing the proposed training with teacher forcing raises MAE from 66.7 to 101.5; vanilla EM solver raises it to 85.6.

Measured effects reported in the paper

Surprising findings

• Teacher forcing hurts substantially compared with feeding conditional-mean predictions during training (MAE 101.5 vs 66.7 in ablation).

Limitations

• Likelihood truncated at κ=5 jumps per step is an empirical choice with a bound that only characterizes decay rate.
• Gains over flow matching on SafeGraph&Advan mean metrics are marginal; the main advantage appears in best-of-K and probabilistic metrics.
• Evaluated only on a synthetic scalar MJD and two real datasets; the proprietary SafeGraph&Advan data limits reproducibility.

Experimental setup

Datasets: synthetic Merton jump diffusion paths SafeGraph&Advan S&P 500

Benchmarks: synthetic MJD dataset SafeGraph&Advan S&P 500

Metrics: MAE MSE R-squared minMAE minMSE maxR2 p-MAE p-MSE p-R2

Baselines: ARIMA Black-Scholes Merton jump diffusion XGBoost MLP GCN DDPM EDM Flow matching NeuralCDE LatentSDE NJ-ODE

Builds on: Merton jump diffusion Black-Scholes model DDPM flow matching Graphormer

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