Inference for a change‐point problem under an OU setting with unequal and unknown volatilities

Abstract

An Ornstein–Uhlenbeck (OU) process is employed as a versatile model to capture the mean‐reverting and stochastic evolution of many variables in various fields of applications including finance and economics. Within the OU setting, we develop a new estimation method to determine the unknown change‐point location under the assumption that the volatilities before and after the change point in a time series are unequal. Our method hinges on the concept of a weighted least sum of squared errors approach and enhanced by a fusion of an iterative algorithm. The consistency of the change‐point estimator is established. This article highlights a numerical implementation on simulated and observed financial market data demonstrating the significant flexibility and accuracy of our proposed modelling and estimation method. The Canadian Journal of Statistics 48: 62–78; 2020 © 2019 Statistical Society of Canada