On monitoring of environmental and other autoregressive processes

Abstract

Statistical surveillance is used for monitoring a sequence of data arriving step by step. These techniques have been applied in many places in society and lately the interest and need for rational methods to be used on environmental data have been growing. In many cases, both for environmental time series and time series from other applications, the data is not independent. This is a violation against the requirements for most standard tools that are used in practice and have to be handled in some way. This licentiat thesis consists of two parts: A case study on fish catches (1) and a study of the properties of some methods used to monitor time series (2).

In the first paper, a case concerning past data from landed catches of six economically interesting fish species in Lake Miilaren in central Sweden is studied. In 1990 the catches of vendace (Coregonus albula) suddenly dropped and the question discussed is whether statistical process control methods are useful for monitoring similar data. The data is examined from both univariate and multivariate viewpoints. In the univariate part, the construction of an alarm procedure for a change in the mean in an AR(l) process is briefly discussed, with this application in mind. The main conclusion is that statistical methods could have been useful for this application. In the second paper, comparisons between two methods often suggested in literature to be used for AR( 1) processes are presented. Further, comparisons are made with a direct Shewhart and a likelihood ratio based method. We can conclude that neither of the two main alternatives studied here is uniformly the best choice. The residual method works best for immediate detection.