> [!tldr] > A SARIMA Model $\mathrm{SARIMA}(p,d,q) \times (P,D,Q)_{s}$ is a stochastic process $(X_{t})$ where the difference term $W_{t}:= \nabla^{d}\nabla_{s}^{D}X_{t}$ is satisfy the model $\phi_{p}(B)\Phi_{P}(B^{s})W_{t} = \theta_{q}(B)\Theta_{Q}(B^{s})Z_{t}$with $(Z_{t})$ being a [[Purely Random Processes|PRP]] and subscripts indicating the order of the polynomials. A SARIMA process can be modeled in R by first taking seasonal differences $\nabla_{s}^{D}$ for appropriate $D$ (usually 0 or 1), then modeling the difference with an non-seasonal $\mathrm{ARIMA}$ model using `arima()`.