Productivity is a critical performance index of process resources. As successive history productivity data tends to be auto-correlated, time series prediction method based on Auto-Regressive Integrated Moving Average (ARIMA) model was introduced into software productivity prediction by Humphrey et al. In this paper, a variant of their prediction method named ARIMAmmse is proposed. This variant formulates the ARIMA parameter estimation issue as a minimum mean square error (MMSE) based constrained optimization problem. The ARIMA model is used to describe constraints of the parameter estimation problem, while MMSE is used as the objective function of the constrained optimization problem. According to the optimization theory, ARIMAmmse will definitely achieve a higher MMSE prediction precision than Humphrey et al?s which is based on the Yule-Walk estimation technique. Two comparative experiments are also presented. The experimental results further confirm the theoretical superiority of ARIMAmmse.