E16.1 This exercise is an extension of Empirical Exercise 14.1. On the text website, www.pearsonglobaleditions.com/Stock_Watson, you will find the data file USMacro_Quarterly, which contains quarterly data on several macroeconomic series for the United States; the data are described in the file USMacro_Description. Compute inflation, Infl, using the price index for personal consumption expenditures. For all regressions use the sample period 1963:Q1–2012:Q4 (where data before 1963 may be used as initial values for lags in regressions).

a. Using the data on inflation through 2012:Q4 and an estimated AR(2)

model:

i. Forecast ΔInfl2013:Q1, the change in inflation from 2012:Q4 to 2013:Q1.

ii. Forecast ΔInfl2013:Q2, the change in inflation from 2013:Q1 to 2013:Q2. (Use an iterated forecast.)

iii. Forecast Infl2013:Q2 − Infl2012:Q4, the change in inflation from 2012:Q4 to 2013:Q2.

iv. Forecast Infl2013:Q2, the level of inflation in 2013:Q2.

b. Repeat

(a) using the direct forecasting method.

c. In Exercise 14.1 you carried out an ADF test for a unit root in the autoregression for Infl. Now carry out the unit root test using the DF-GLS test. Are the conclusions based on the DF-GLS test the same as you reached using the ADF test? Explain.