Regime switching detection for the Levy driven Ornstein–Uhlenbeck process using CUSUM methods

The article considers using a trending Ornstein–Uhlenbeck process, driven by a Levy process, for modeling financial time series. The authors demonstrate that the Levy driven model gives more flexibility to describe financialtime series than the simple classical model. In particular, the Levy driven model allows modeling distributions with heavy tails, which is a common property of time series in real applications. The authors describe efficient methods for estimating model parameters using such methods as OLS (ordinary least squares) and RLS (regularized least squares). The article also solves the regime switching problem in a real time data stream. The authors built an algorithm based on CUSUM (CUmulative SUM) methods that is capable of determining regime switches consecutively as they happen online and keep model parameters up to date. Solution of the regime switching problem is important in real applications, since the dynamics of real systems tend to change over time under the influence of external factors.