Tutorial 3: AR(p) Models
Question 1 (Computer)
Consider again the Worksheet โCPIEmpโ from the dataset โUSData.xlsxโ on the KEATS page.
a) Import the data and prepare it for time series analysis by setting a time series variable
using tsset
b) Generate a variable for CPI inflation, ๐๐ถ๐๐ผ๐ก=100ฮln ๐ถ๐๐ผ๐ก, the same as last week
c) Run seven different AR(p) models with lags increasing from ๐ = 0 to ๐๐๐๐ฅ = 6. The
last model is:
๐๐ถ๐๐ผ๐ก= ๐ฝ0+ ๐ฝ1๐๐ถ๐๐ผ๐กโ1 + โฏ+ ๐ฝ6๐๐ถ๐๐ผ๐กโ6 + ๐ข๐ก
IMPORTANT: Be careful to use same number of observations in each regression!
d) Store the results for each of the seven regressions, calling them AR0 through AR6 and
generate a table of statistics including the AIC and BIC (see lecture notes). Which
model do you choose using AIC/BIC?
e) Make a one-step ahead point and interval forecast for inflation based on the model
selected by the BIC. Now use these results to back out the level forecast of the CPI (i.e.
reverse the growth rate transformation). How do you interpret this short-run prediction?
Question 2 (Computer)
Repeat the analysis in Question 1 for the CPI food variable. Do you find the same model to be
selected for CPI food? Are there any issues that you encounter?
Question 3 (Problem)
a) Rewrite the following processes without the lag operator:
i. (1 โ ๐ฝ1๐ฟ)๐
๐ก= ๐ฝ0+ ๐ข๐ก
ii. (6 โ 5๐ฟ + ๐ฟ2)๐
๐ก= ๐ข๐ก
b) Rewrite the following processes with the lag operator:
i. ๐
๐ก= 5 + 1.5๐
๐กโ1 โ 0.5๐
๐กโ2 + ๐ข๐ก ๐ฅ
ii. ๐
๐ก= 1 + 0.1๐
๐กโ12 + ๐ข๐ก
c) Determine whether the processes in parts (ai), (aii) and b(i) ๐ฅ are stationary.
d) What kind of data might we be using if we were specifying a model like (bii)?
e) Assuming the known parameter values in a), and if we are given data such that ๐
๐=
0.5 and ๐
๐โ1 = 1, then what are the optimal point forecasts for ๐
๐+1 in parts (ai) and
(aii)? What information would we need to produce interval forecasts?
Discuss
Discuss
Intermediate Econometrics - 5QQMN938
Dr Canh Thien Dang