Effectiveness of Joint Estimation When the Outlier Is the Last Observation in an Autocorrelated Short Time Series

Abstract

The effectiveness of the joint estimation (JE) outlier detection method as a process control technique for short autocorrelated time series is investigated and compared with exponentially weighted moving average (EWMA). The research goal is to determine the effectiveness of the method for detecting out‐of‐control observations when they are the last observation in a short autocorrelated time series. This is an important problem because detecting an outlier in the period when it occurs, rather than several periods after it occurs, will preclude the production of more defective units. Two cases are investigated: short simulated time series when normality is assumed, and short real time series when the assumption is violated. The results show that JE is effective for short time series, particularly for autoregressive series when normality is violated. Joint estimation is also effective for moving average series under the normality assumption and less effective when the assumption is violated. In all cases, JE is found to be more effective than EWMA.