5.13\.\* Let St represent the monthly sales data in sales (n = 150), and let Lt be the leading indicator in lead. (a) Fit an ARIMA model to St, the monthly sales data. Discuss your model fitting in a step-by-step fashion, presenting your (A) initial examination of the data, (B) transformations and differencing orders, if necessary, (C) initial identification of the dependence orders, (D) parameter estimation, (E) residual diagnostics and model choice. (b) Use the CCF and lag plots between rSt and rLt to argue that a regression of rSt on rLt3 is reasonable. [Note: In lag2.plot(), the first named series is the one that gets lagged.] (c) Fit the regression model rSt = b0 + b1rLt3 + xt, where xt is an ARMA process (explain how you decided on your model for xt). Discuss your results.