Macro-Econometrics Homework Assignment
3
Macro-Econometrics
Homework Assignment #4 (100 points)
This assignment is based on the U.S. Consumer Price Index (CPI) data in the Excel worksheet HW_Data_Period_4.xlsx , which is found on the course website. You will need to use the quarterly observations, which run from 1957:Q1 to 2017:Q2. There are three variables shown in the quarterly spreadsheet: CPI, the log of CPI, and the annualized growth rate in the CPI (inflation).
(a). Plot the CPI in growth rates (actually the first-difference of the logged data) as a line graph. Does it look stationary? That is, does the mean and variance look to be time-invariant? Why or why not?
(b). Using the full sample for the series in growth rates, estimate the models shown in the table on the next page. You do not need to show your results, but be sure that you have replicated the results in the table. Keep in mind that there might be some differences in your results from those in the table due to round-off errors or to the use of a different software package.
c). One of the rows in the table shows the sum of squared residuals (SSR). Please explain briefly why this is an unreliable measure for choosing an optimal regression fit.
d). In a few sentences explain the three categories of model selection that were described in the book and lecture and how those categories might be measured in practice.
e). The models in columns (1)-(3) are AR models, with lag lengths ranging from 1 to 4. How would you evaluate these three models based on your answer to part d and based on the information provided in the table?
f). The models in columns (4)-(6) are ARMA models, with one MA lag added to the models in columns (1)-(3)lengths. How would you evaluate these three models based on your answer to part d and based on the information provided in the table?
(g). Now, considering all six models, what would be your choice for the “best” model? Use your answers to parts e and f to justify your choice.
(1)(2)(3)(4)(5)(6)
p=1p=2p=4p=1p=2p=4
q=0q=0q=0q=1q=1q=1
α03.593.553.443.463.473.479
6.014.012.402.772.802.805
α10.770.500.400.950.91-0.341
26.6313.2710.4856.059.67-8.775
α20.360.200.040.551
9.474.860.5310.772
α30.010.247
0.206.236
α40.290.349
5.797.286
β1-0.53-0.500.948
-13.01-5.9534.732
SSR683.506595.147533.101569.281568.916462.000
AIC3.9093.7803.6883.7363.7443.560
SBC3.9523.8383.7753.7943.8163.661
Q(4)0.0000.0000.3140.0000.0010.891
Q(8)0.0000.0000.0230.0000.0000.941
Q(12)0.0000.0000.0020.0000.0000.194
NOTES:
1. The numbers in bold italics are t-statistics for the null hypothesis that the associated coefficient is equal to zero.
2. SSR is the sum of squared residuals.
3. AIC and SBC are the Akaike and Schwartz Bayesian selection criteria, respectively.
4. The numbers in the Q(n) rows indicate the p-values for the Ljung-Box Q statistic for the autocorrelations of n lags of
the model residuals.
Estimated Models of the Consumer Price Index
(Dep. Var = Annualized Percent Change)