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This paper considers a supply chain with the first order autoregressive and the first order moving average (ARMA (1,1)) demand.The lead time demand is estimated using the minimum mean-square error (MMSE) forecasting technique.The expression of the bullwhip effect for a two stage supply chain consisting of one supplier and one retailer is derived,and the existence condition of the bullwhip effect as well as the impact of demand information sharing on the bullwhip effect are analyzed theoretically and numerically.At last,the extension analysis for bullwhip effect in a multiple stage supply chain is performed by using numerical examples.