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$rate
x=da[,5:9]/100 # divided by 100 to ensure numerical stability.
model1=lm(unrate~icm1, data=x)
summary(model1)
par(mfcol=c(2,1))
acf(model1$residuals, lag=36)
pacf(model1$residuals, lag=36)
2. Assume now that the residual follows a seasonal ARIMA model. For simplicity, assume that our model is (p, 0, q) (1, 0, 1)12. Also assume that 2 p 4 and 2 q 5. Find out the best model by perform regression with time series errors, and checking the estimated coefficients as well as AIC scores. Check if the model is adequate. A sample code is
model2=arima(unrate, order=c(2,0,2),xreg=x[,5],seasonal=list(order=c(1,0,1), period=12))
3. Now we use the weekly initial jobless claims. First run a multiple regression between unrate with the four weekly numbers w1m1 w2m1 w3m1 w4m1 and the monthly cliam "icm1". Select the significant variables from this regression. ( Note, this is just to judge the which of the weeks are important to include, not to obtain estimates).
4. Run a time series regression of unrate with the selected variables from the last step using the arima command. For simplicity, assume that the residuals follow (2, 0, 2) (1, 0, 1)12. Perform model diagnosis, and check model adequacy. (You can certainly run a loop to select the proper p and q values for the ARMA. But it's not required for the homework, you can simply use 2 and 2.)
5. Compare the AIC scores of the model obtained in step 2 and 4.