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The bullwhip effect in a multistage supply chain was analyzed using sophisticated stationary forecasts (third order moving average and third order exponential smoothing forecasts ). The third order exponential smoothing and third order moving average forecasts sometimes have a variance reducing effect on the supply chain.In a supply chain with positively correlated or independent and identically distributed (i. i. d) demands, the order variance based on simple moving average forecast (or simple exponential smoothing forecast) is larger than the order variance based on second order moving average forecast (or second order exponential smoothing forecast) ,and the order variance based on second order moving average forecast ( or second order exponential smoothing forecast) is larger than the order variance based on third order moving average forecast( or third order exponential smoothing forecast). In addition, for i.i.d demands, third order exponential smoothing forecast leads to a larger variation than third order moving average forecast.