A Partially Hidden Markov Model of Customer Dynamics for CLV Measurement

Abstract

Customer lifetime value (CLV) measurement is challenging as it requires forecasting customers' future purchases. Existing stochastic CLV models for this purpose generally make the following assumptions: 1) purchase behavior of customers can be described by purchase frequency and the average monetary value of transactions, 2) customers keep the same purchase behavior pattern over time, 3) purchase frequency and monetary value are independent, and 4) customers are active during a limited period of time after which they permanently defect. We develop a new stochastic model that relaxes these four assumptions. First, in addition to the number of transactions and its monetary values, we also model purchase incidence decisions (i.e. whether or not to purchase). Second, our partially hidden Markov truncated–NBD-GG (PHM/TNBD-GG) model allows dynamic purchase patterns, dependence between purchase frequency and monetary value, and customers to become active after a few periods of temporary inactivity. Validation of our model on two datasets demonstrates that if assumptions 1 to 4 of existing stochastic models are violated our model produces more accurate forecasts of future customer behavior.