Long-Memory Reservoir Computing for Data-Scarce Dengue Forecasting

2026-07-13

AI Summary

Dengue incidence time series present significant challenges due to their short length, high noise levels, non-stationarity, nonlinearity, and long-range dependence, which conventional methods struggle to model simultaneously. This work introduces, for the first time, a statistically grounded long-memory mechanism into reservoir computing, proposing two novel echo state network architectures—fESN and wESN—that explicitly capture long-range dependencies through fractional differencing and wavelet smoothing, respectively. Coupled with ridge regression readout layers and conformal prediction, the framework yields calibrated prediction intervals without requiring distributional assumptions. Theoretical analysis ensures closed-loop dynamical stability, and extensive experiments demonstrate that the proposed approach consistently outperforms existing statistical and deep learning baselines across multiple dengue datasets and varying forecast horizons.

Abstract

Accurate dengue forecasting is crucial for public health planning, but remains challenging because incidence series are often short, noisy, non-stationary, nonlinear, and often affected by long-range temporal dependence. Fractional differencing in Autoregressive Fractionally Integrated Moving Average (ARFIMA) helps balance non-stationarity and persistence, but its linear structure limits its ability to capture nonlinear dynamics. Deep neural networks can model nonlinear patterns, but usually require large training samples and do not explicitly encode statistical long memory. Echo State Networks (ESNs), a widely used reservoir computing framework, are attractive in this setting because they retain nonlinear recurrent dynamics while training only a simple readout, making them suitable for data-scarce scenarios. However, standard ESNs lack long-term memory from a time-series perspective. This study proposes a long-memory reservoir computing framework that integrates dedicated long-memory and short-memory ESN reservoirs with a ridge-regression readout. We introduce two variants: Fractional ESN (fESN), which incorporates fractional-differencing dynamics into the reservoir to encode long-range dependence directly, and Wavelet ESN (wESN), which extracts stable low-frequency components through wavelet smoothing before modeling them with a memory-aware reservoir. We establish theoretical guarantees for closed-loop reservoir dynamics, showing that standard ESNs induce short-memory processes under mild conditions, whereas the proposed long-memory reservoirs generate polynomially decaying dependence consistent with statistical long memory. Across multiple dengue datasets and forecasting horizons, fESN and wESN outperform statistical and deep learning baselines. Combining conformal prediction with fESN and wESN provides distribution-free calibrated uncertainty intervals.

Problem

• dengue forecasting
• long-memory
• time series
• data scarcity
• nonlinear dynamics

Innovation

• long-memory reservoir computing
• fractional ESN
• wavelet ESN
• dengue forecasting
• conformal prediction