3. (20 points) Download the Case-Shiller Home price index for Chicago from FRED (or via STATA ) https://fred.stlouisfed.org/series/CHXRSA and calculate the return associated with this series. [the original data source is here https://fred.stlouisfed.org/series/CHXRNSA or at http://www.standardandpoors.com/home/en/us/). Note that, CHXRNSA is the raw, unadjusted series and CHXRSA is the seasonally adjusted series. The seasonally adjusted series removes the cyclical variation that repeats itself year after year (Le. summer tends to have higher prices than the winter). For this question, you want to use the seasonally adjusted series. (a) Examine the ACF and PACF of the adjusted returns. Do you see the same pattern? (b) Fit an AR(1) model to this data. Examine the residual autocorrelations. (Use adjusted returns) (c) Build the one-step ahead forecast for every observation in the sample using your fitted AR(1) model. Plot the forecast and the real data on the same plot. (Use adjusted returns) (d) What is one-step ahead out of sample forecast (ie. the forecast of T+1) and find the 95% prediction interval. (Use adjusted returns)