Statistical properties and economic implications of jump‐diffusion processes with shot‐noise effects

The shot‐noise jump‐diffusion (SNJD) model aims to reflect how economic variables respond to the arrival of sudden information. This paper analyzes the SNJD model, providing its statistical distribution and closed‐form expressions for the characteristic function and moments. We also analyze the dynamics of the model, concluding that the degree of serial autocorrelation is related to the occurrence and magnitude of abnormal information. In addition, we provide some useful approximations in a particular case that considers exponential‐type decay. Empirically, we propose a GMM approach to estimate the parameters of the model and present an empirical application for the stocks included in the Dow Jones Averaged Index. Our findings seem to confirm the presence of shot‐noise effects in 73% of the stocks and a strong relationship between the shot‐noise process and the autocorrelation pattern embedded in data.