The paper considers a closed-loop supply chain with one supplier, one manufacturer and two retailers, in which the customer demand is assumed to be price-sensitive. We induce price in the demand through an auto-regressive moving average (ARMA) pricing process, and characterize the demand by an auto-regressive non-standard ARMA process. We use an order-up-to inventory policy with minimum mean square error forecasting scheme and derive the expression for the bullwhip effect at each echelon of the closed-loop supply chain. With the help of numerical simulation, we recognize that the bullwhip effect or the anti-bullwhip effect may occur depending on critical values of parameters of the underlying demand process. We observe that the bullwhip effect at the manufacturer is affected by retailer's market share. Moreover, a remanufacturing process in the reverse channel and a steady pricing mechanism for the product can significantly reduce the bullwhip effect.