Nonparametric estimator for the time of a step change in the trend of random walk models with drift

Living systems tend to have non-normal behaviors, are autocorrelated, exhibit patterns of growth or decrement, and achieve states of dynamic equilibrium, making them hard to manage. One way to manage and improve these complex systems is by identifying assignable causes of variation whenever they occur, and control charts are one of the most known tool for those situations. However, in the presence of sustained changes, control charts are not capable of telling the initial moment of a change. This paper proposes a nonparametric estimator capable of dealing with non-normal observations heterocedastic over time. The median test is used to estimate the time of a step change in Shewhart Control Charts using a relatively successful approach based on a binary segmentation approach. Furthermore, an application is developed to deal with changes on the trend of processes fitting a random walk with drift. Performance is evaluated with extensive Monte Carlo simulations, and results are compared with the maximum likelihood estimator for normal series of independent observations. Results showed acceptable performance when normality is not met and robustness under heterocedasticity.