Transient detection with an application to a chemical process

We propose a sequential test procedure for transient detections in a stochastic process which can be expressed as an autoregressive moving average (ARMA) model. Preliminary analysis shows that if an ARMA(p,q) time series exhibits a transient behavior, then its residuals behave as an ARMA(Q,Q) process, where Q ≤ p + q. Based on this fact, we derive a new sequential test to determine when a transient behavior occurs in a given ARMA time series. Simulation experiments conducted in this study show that the proposed test can detect the occurrence of a transient in the ARMA model. We also apply the proposed method to detect transient changes in the pH of an erythromycin salt.