This paper considers how various types of Markov chains can be used to help forecast the purchase behaviour of customers. The models are used in a case study of the purchase behaviour of the customers of a major insurance company.As well as looking at the impact of relaxing the first order Markov and time homogeneity assumptions which are usually used in Markov chain models, the paper also looks at models based on mover-stayer ideas and ones which enlarge the state space by including the type of purchase as well as the time of purchase. One important aspect of long term customer relationships such as those which occur in the insurance and assurance industry is the impact of changes in the economy. The final section show how these can be incorporated into Markov chain models and how they can make a significant difference to the quality of the predictions.
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