6. External Regressors and Model Improvements (Written Report) PLEASE ANSWER QUESTION 3!!

PLEASE ANSWER QUESTION 3!!

Include your answers to this question in your written report. External Regressors Next, we will include monthly BER data as an external regressor to try to improve the predictions of inflation rate. Here we only consider to add one BER term in the AR(p) model of CPI inflation rate. In specific, we model the CPI inflation rate Xt by X+ = OiXt-i + XYt-, + Wt, 2=1 where Yt is the BER inflation rate at time t, r > 0 is the lag of BER rate w.r.t. CPI rate, and Wt is white noise. which find r, i.e., the lag 1. (4 points) Plot the cross correlation function between the CPI and BER inflation rate, between two inflation rates. (As only one external regressor term is involved in the model, we only consider the peak in the CCF plot.) Note: In general, multiple external terms 2214;Yt-r; can be incorporated in the model if there are multiple peaks in CCF plots. i= 2. (3 points) Fit a new AR model to the CPI inflation rate with these external regressors and the most appropriate lag. Report the coefficients. Python Tip: You may use sm.tsa.statespace. SARIMAX. 3. (3 points) Report the mean squared prediction error for 1 month ahead forecasts. Include your answers to this question in your written report. External Regressors Next, we will include monthly BER data as an external regressor to try to improve the predictions of inflation rate. Here we only consider to add one BER term in the AR(p) model of CPI inflation rate. In specific, we model the CPI inflation rate Xt by X+ = OiXt-i + XYt-, + Wt, 2=1 where Yt is the BER inflation rate at time t, r > 0 is the lag of BER rate w.r.t. CPI rate, and Wt is white noise. which find r, i.e., the lag 1. (4 points) Plot the cross correlation function between the CPI and BER inflation rate, between two inflation rates. (As only one external regressor term is involved in the model, we only consider the peak in the CCF plot.) Note: In general, multiple external terms 2214;Yt-r; can be incorporated in the model if there are multiple peaks in CCF plots. i= 2. (3 points) Fit a new AR model to the CPI inflation rate with these external regressors and the most appropriate lag. Report the coefficients. Python Tip: You may use sm.tsa.statespace. SARIMAX. 3. (3 points) Report the mean squared prediction error for 1 month ahead forecasts