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This paper proposes a second-order jump diffusion model to study the jump dynamics of stock market returns via adding a jump term to traditional diffusion model. We develop an appropriate maximum likelihood approach to estimate model parameters. A simulation study is conducted to evaluate the performance of the estimation method in finite samples. Furthermore, we consider a likelihood ratio test to identify the statistically significant presence of jump factor. The empirical analysis of stockdoi:10.1155/2018/9549707 fatcat:z4njtmgkrvgobkzo2hqkmvui44