Fraud detection describesmethods that attempt to identify fraudulent activity as quickly as possible. From a statistical methods perspective there are broadly two approaches to fraud detection [1]. These relate to whether we intend to detect known examples of fraudulent activity or whether we intend to detect novel forms of fraudulent behaviour. In the former case pattern matching techniques are used in the latter case anomaly detection techniques are deployed.

Peer group analysis is an unsupervised method for monitoring behaviour over time [2] and it can be used for anomaly detection [3]. In the context of plastic card fraud detection, peer groups are built for each account, where a peer group is collection of other accounts that behave similarly. The subsequent behaviour of each account is measured in relation to its peer group. Should an account’s behaviour deviate strongly from its peer group then the account is flagged as anomalous and its recent transactions are flagged as potential frauds. This approach differs from the usual anomaly detection methods where each account’s current behaviour is measured in relation to its own past behaviour. We show how to apply peer group analysis to times series that consist of timealigned multivariate continuous data. The initial analysis comprises of a method to determine the peer group members for each time series. For this we need to compare time series [4], we describe one method that is useful for plastic card transaction data. Once we have the peer groups, the analysis then comprises of a method for tracking a time series with respect to its peer group. An anomaly is said to have occurred should the separation between the time series and its peer group exceed some externally set threshold. Account histories of plastic card transaction data are neither time aligned nor do they consist of purely continuous data. A transaction can occur at any time and each transaction has associated with it a record containing a large amount of information. This enables the card issuer to distinguish between the large number of possible transaction types that can occur. For example an account holder who checks their balance at an ATM (an example of a transaction where no money is transferred) or an account holder who purchases a rental car but was not present at the point of sale. We describe one way to time align different account transaction histories and to transform some pertinent information into continuous variables. We summarise experiments performed using peer group analysis on real credit card transaction data. In particular we examine the effect that missed fraudulent transactions have on the performance of the peer groups. We describe a method for robustifying against fraudulent transactions contaminating peer groups.We present our results using a new measure of performance that has been designed specifically for plastic card fraud [5]. Not all accounts can be tracked well enough by their respective peer groups to usefully identify anomalous behaviour.We describe a measure of peer group quality which we use to identify accounts that are more likely to be successfully analysed using peer groups.