5.11 The file labeled clim-hyd has 454 months of measured values for the climatic variables air temperature, dew point, cloud cover, wind speed, precipitation (pt), and inflow (it), at Shasta Lake. We would like to look at possible relations between the weather factors and the inflow to Shasta Lake.

(a) Fit ARIMA(0, 0, 0)×(0, 1, 1)12 models to (i) transformed precipitation Pt =

√

pt and (ii) transformed inflow It = logit.

(b) Apply the ARIMA model fitted in part

(a) for transformed precipitation to the flow series to generate the prewhitened flow residuals assuming the precipitation model. Compute the cross-correlation between the flow residuals using the precipitation ARIMA model and the precipitation residuals using the precipitation model and interpret. Use the coefficients from the ARIMA model to construct the transformed flow residuals.