Jump amplitude inference in SDEs with cosine kernel

For estimating the jump amplitude in stochastic differential equations with jumps, existing parameter estimation methods in the academic community suffer from inherent systematic errors. Commonly used kernel functions often assume symmetric distributions, limiting their ability to model skewed distributions. Many methods can simulate positively skewed distributions but fail to handle negatively skewed ones, and they tend to overestimate the probability density when the jump size is close to zero. This paper introduces a novel kernel density estimation method based on cosine functions for jump amplitude estimation. Our approach addresses these systematic errors, especially under large sample conditions, enabling more accurate statistical inference for the jump amplitude in stochastic differential equations with jumps. We anticipate that this method will contribute positively to research in areas such as finance and signal processing.