Efficient CNN-LSTM Based Parameter Estimation of Lévy Driven Stochastic Differential Equations

This study addresses the challenges in parameter estimation of stochastic differential equations (SDEs) driven by non-Gaussian noises, which are critical in understanding dynamic phenomena such as price fluctuations and the spread of infectious diseases. Previous research highlighted the potential of LSTM networks in estimating parameters of a-stable Levy driven SDEs, but faced limitations including high time complexity and constraints of the LSTM's chaining property. To mitigate these issues, we introduce the PEnet, a novel CNN-LSTM based three-stage model that offers (a) an end-to-end approach with superior accuracy and adaptability to varying data structures, (b) enhanced inference speed for long-sequence observations through initial data feature condensation by CNN, and (c) high generalization capability, allowing its application to various complex SDE scenarios. Experiments on synthetic datasets confirm PEnet's significant advantage in estimating SDE parameters associated with noise characteristics, establishing it as a competitive method for SDE parameter estimation in the presence of Levy noise.