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Bayesian Forecasting of an Inhomogeneous Poisson Process With Applications to Call Center Data

A call center is a centralized hub where customer and other telephone calls are handled by an organization. In today's economy, call centers have become the primary points of contact between customers and businesses. Thus accurate predictions of call arrival rates are indispensable to help call center practitioners staff their call centers efficiently and cost-effectively. This article proposes a multiplicative model for modeling and forecasting within-day arrival rates to a U.S. commercial bank's call center. Markov chain Monte Carlo sampling methods are used to estimate both latent states and model parameters. One-day-ahead density forecasts for the rates and counts are provided. The calibration of these predictive distributions is evaluated through probability integral transforms. Furthermore, 1-day-ahead forecasts comparisons with classical statistical models are given. Our predictions show significant improvements of up to 25% over these standards. A sequential Monte Carlo algorithm is also proposed for sequential estimation and forecasts of the model parameters and rates.