The Use of Exponentially-Smoothed Transition Matrices to Improve Forecasting of Cash Flows from Accounts Receivable

A pioneering application of a Markov chain to forecast account receivable flows (Cyert, Davidson, and Thompson [Cyert, R. M., H. J. Davidson, G. L. Thompson. 1962. Estimation of the allowance for doubtful accounts by Markov chains. Management Sci. (August) 287-303.]) employed an unusual (the oldest balance) method of aging accounts and an assumption that the resulting transition matrix was stable. Forecasting steady state results was the primary focus of the application. The present research uses a commonly found (partial balance) method of aging, an assumption of dynamic changes in the transition matrix, and does not focus on steady state results. A manufacturer's data were analyzed and exponential smoothing was introduced to update the average transition matrix thereby enabling a tracking of changing customer payment behavior. The actual and Markovian estimates of the company's cash collections checked favorably. The paper also discusses how modifications such as the seasonal and trend adjustments introduced by Winters (Winters, P. R. 1960. Forecasting sales by exponentially weighted moving averages. Management Sci. (April) 324-342.) may be incorporated into the model. Extensions to other areas are offered.