We develop a stochastic calculus that makes it easy to capture a variety of predictable transformations of semimartingales such as changes of variables, stochastic integrals, and their compositions. The framework offers a unified treatment of real-valued and complex-valued semimartingales. The...

The paper introduces a simple way of recording and manipulating general stochastic processes without explicit reference to a probability measure. In the new calculus, operations traditionally presented in a measure-specific way are instead captured by tracing the behaviour of jumps (also when no...

Testing the performance of statistical models with historical time series requires a careful handling of the data. Even if a dataset is seemingly completely separated in an in-sample and an out-of-sample set information may be leaked. Such leakage can lead to a significant overestimation of the...