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The data set contains quarterly data from 1959q1 to 2016q4 for PCEP, the price index for personal consumption expenditures from the U.S. National income and Product Accounts. There is another variable in the data set, PCEPxFE, which is the same index minus food and energy, but we won’t be using that variable.
The data are From the FRED website, a rich source of macroeconomic data. Here’s a graph of PCEP: https://fred.stlouisfed.org/graph/?g=doaT (Links to an external site.)
Links to an external site.
a. Generate the annualized inflation rate, Infl =400. x [ In (PCEPt) – In (PCEPt-1)] . (Note: In Stata, upper/lower case matters — Infl is not the same as infl).
Test for a unit root in Infl using the augmented Dickey-Fuller test. Use three AR lags. (Unless directed otherwise, use the sample period 1963q1 – 2012q4 for all problems in this assignment.).
The t-statistic for the ADF test is _____ (three decimal places). It is (significant/insignificant)______ at the 5% level. Thus, there is evidence (for/against)_____ a unit root in Infl.
b. To eliminate the unit root in inflation, we can difference the data. Create the variable ∆Infl and test for a unit root in ∆Infl using the augmented Dickey-Fuller test. Use 2 AR lags when carrying out the test.
The t-statistic for the ADF test is _____ (three decimal places). It is (significant/insignificant) ______at the 5% level. Thus, there is evidence (for/against) ______a unit root in ∆Infl — it appears to be______ (stationary/non-stationary) .
c. Find the first four autocorrelations of ∆Infl.
The first is _______(four decimal places) .
The fourth is ______(four decimal places) .
(Note: Section 11.4.4 of this guide, along with other sections, might be helpful for this homework.)
What lag length is chosen by BIC? _________
The minimum BIC statistic is ________(four decimal places) .
What lag length is chosen by AIC? __________
The minimum BIC statistic is ________ (four decimal places) .
e. Use an AR(2) model for ∆Infl to forecast ∆Infl for 2017q1 (estimate the model through 2012q4, then forecast ∆Infl for 2017q1).
The forecast for ∆Infl in 2017q1 is _________(four decimal places) .
f. Use an AR(2) model for ∆Infl to generate pseudo forecasts for the period 2012q1 through 2016q4. To do this, estimate the model through 2011q4 and forecast ∆Infl for 2012q1. Then estimate the model through 2012q1 and forecast 2012q2, and so on. The last regression will estimate the model through 2012q3 and forecast for 2012q4.
The forecast for 2015q1 is _________(four decimal places) .
The forecast for 2016q4 is _________ (four decimal places) .
g. What is the RMSE?
The RMSE is _________(four decimal places) .
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