We characterize jump dynamics in U.S. stock market returns using a novel series of intraday prices covering almost 90 years. Jump vary substantially over time. Trends activity relate to secular shifts the nature news. Unscheduled news often involving major wars drives early decades, whereas scheduled and especially pertaining monetary policy recent decades. variation measures forecast excess re...

We propose a general framework for studying statistics of jump-diffusion systems driven by both Brownian noise (diffusion) and a jump process with state-dependent intensity. Of particular natural interest in many physical systems are the jump locations: the system evaluated at the jump times. As an example, this could be the voltage at which a neuron fires, or the so-called ‘threshold voltage’....

The diffusion of a walk in the presence of traps is investigated. Different diffusion regimes are obtained considering the magnitude of the fluctuations in waiting times and jump distances. A constant velocity during the jump motion is assumed to avoid the divergence of the mean squared displacement. Using the limit theorems of the theory of Lévy stable distributions we have provided a characte...

The paper is devoted to forecasting hourly day-ahead electricity prices from the perspective of existence jumps. We compare results different jump detection techniques and identify common features price apply jump-diffusion model with a double exponential distribution sizes explanatory variables. In order improve accuracy forecasts, we take into account time-varying intensity occurrences. forec...