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For checking the Granger's Causality between two variables of a data-set, lets say to check X granger-causes Y, we create two regression models, a restricted model(containing the lagged values of only Y) and a full model(containing the lagged values of only Y as well as X) for predicting the current value of Y. We compare these two regression model to check if using lagged values of X provides some additional explanatory information. My question is, do these regression models need to linear for the purpose above(with degree = 1 for X and Y) or the models can be polynomial(degree > 1) ?

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