What is a good index? Problems with statistically based indicators and the Malmquist index as alternative.

Conventional multivariate statistical methods have been used for decades to calculate environmental indicators. These methods generally work fine if they are used in a situation where the method can be tailored to the data. But there is some skepticism that the methods might fail in the context of skewed data distributions or spatial auto-correlation. Further, the indicators developed by statistical approaches can not be used to compare different regions or time periods that had not been covered by the input data. The aim of the paper is to demonstrate some of the shortcomings and to identify how the Malmquist index might be used as an alternative. The paper presents the results of an exhaustive review in the field of environment, hydrology and water quality which identified the most commonly used approaches. Then principal component analysis as representative of these approaches and the Malmquist index are challenged with simulated time series data to demonstrate the failure of statistical methods in two of the most common problems faced in construction of a water quality index.