We have run seasonal arma model on the unemployment rate data. Now con- sider adding the weekly initial jobless claim to predict the monthly unem- ployment rates. The data is from 1967 to 2010. The data is given in "m- unrateic.txt". As shown below, the column "rate" denotes the unemployment rate, and the 5th to 8th column denotes the weekly jobless claims from week 1 to week 4 of the month and the last column-"icml" is the total number of initial jobless claim of the month. > da=read . table("m-unrateic. txt", header=T) > > head (da) year mon dd rate wimi w2ml w3m1 w4m1 icm1 1 1967 2 1 3.8 208 207 217 204 836 2 1967 3 1 3.8 216 229 242 916 3 1967 4 1 3.8 310 241 245 247 1043 4 1967 5 1 3.8 3 259 257 299 245 1315 5 1967 6 1 3.9 254 231 230 228 943 6 1967 7 1 3.8 248 238 224 218 928 1. Perform a simple regression of unrate with the monthly claim numbers using the following commands. Comment on the results of the regression and the acf/pacf plots. unrate=da$rate x=da [, 5:9]/100 # divided by 100 to ensure numerical stability. model1=1m (unrate icm1, data=x) summary (model1) par (mfcol=c (2,1)) acf (model1$residuals, lag=36) pacf (model1$residuals, lag=36) 2. Assume now that the residual follows a seasonal ARIMA model. For sim- plicity, assume that our model is (p, 0, q) x (1, 0, 1)12. Also assume that 2