An MCMC based Bayesian inference approach to parameter estimation of distributed lag models for forecasting used product returns for remanufacturing

Forecasting the quantity and timing of used product returns is one of the major challenges faced by remanufacturers. Distributed lag model has been proposed in recent years to forecast used product returns based on past sales data. However, the forecasting accuracy of a distributed lag model is affected to a large extent by the estimation of the parameters of the lag function. The Bayesian inference approach for parameter estimation which has been proposed by previous studies requires solving the marginal likelihood function which is often difficult even for a slightly complex lag function. In this research, a Markov Chain Monte Carlo (MCMC) based Bayesian inference approach is proposed to estimate the parameters of a lag function which provides an efficient way to sample parameter values from a posterior distribution regardless of the complexity of a lag function. An example case study of forecasting used product returns was undertaken to illustrate the proposed parameter estimation approach which was validated by comparing it with the maximum likelihood estimate (MLE) method. The validation results show that the forecasting accuracy of the number of used product returns based on the parameters estimated by using the proposed MCMC based Bayesian approach is better than that estimated by using the MLE method in terms of mean absolute percent errors and variance of errors.