This is a series where we aim to cover in detail various aspects of the classic Ornstein-Uhlenbeck (OU) model and the Ornstein-Uhlenbeck Jump (OUJ) model, with applications focusing on mean-reverting spread modeling under the context of pairs trading or statistical arbitrage. Given the universality and popularity of those models, the techniques discussed can easily be applied to other areas where the OU or OUJ model seems fit.

In this article, we aim to dive into the classic OU model, and illustrate the most common tasks encountered in applications:

1. How to generate an OU process.
2. Caveats in fitting an OU process.