Robustness of measures of common cause sigma in presence of data correlation

Process monitoring in the presence of data correlation is one of the most discussed issues in statistical process control literature over the past decade. However, the attention to retrospective analysis in the presence of data correlation with various common cause sigma estimators is lacking in the literature. Maragah et al. (1992), in an early paper on the retrospective analysis in presence of data correlation, addresses only a single common cause sigma estimator. This paper studies the effect of data correlation on retrospective X-chart with various common cause sigma estimates in stable period of AR(1) Process. This study is carried out with the aim of identifying suitable standard deviation statistic/statistics which is/are robust to the data correlation. This paper also discusses the robustness of common cause sigma estimates for monitoring the data following other time series models, namely ARMA(1,1) and AR(p). Further, the bias characteristics of robust standard deviation estimates have been discussed for the above time-series models. This paper further studies the performance of retrospective X-chart on forecast residuals from various forecasting methods of AR(1) process. The above studies were carried out through simulating the stable period of AR(1), AR(2), stable and invertible period of ARMA(1,1) processes. The average number of false alarms have been considered as a measure of performance. The results of simulation studies have been discussed.     

Time series analysis of categorical data using auto-mutual information

Despite its importance, there has been little attention in the modeling of time series data of categorical nature in the recent past. In this paper, we present a framework based on the Pegram's [An autoregressive model for multilag Markov chains. Journal of Applied Probabability 17, 350–362] operator that was originally proposed only to construct discrete AR(p$p$) processes. We extend the Pegram's operator to accommodate categorical processes with ARMA representations. We observe that the concept of correlation is not always suitable for categorical data. As a sensible alternative, we use the concept of mutual information, and introduce auto-mutual information to define the time series process of categorical data. Some model selection and inferential aspects are also discussed. We implement the developed methodologies to analyze a time series data set on infant sleep status.