The objective of this paper is to study the impact of seasonal demand parameters and the lead time of the retailer on the variables like order quantity, bullwhip effect and on-hand inventory to elaborate the supply chain dynamics. The objectives are achieved through analysis of a simple two echelon supply chain with retailer at the lower level and the supplier at the upper level. The time series of the end customer demand data exhibit a non-stationary SARIMA process. Through expression of bullwhip effect we show an increase in their value due to the presence of seasonal effect and non-stationary in the end customer demand. Further, a compression of our model with that of Graves has been done, who considers end customer demand as a non-stationary non-seasonal. Our results show an increase in the variance of the expressions of both order quantity and on-hand inventory due to the presence of seasonality in the demand.