Econometrics ADF Test

Question

Suppose that we want to test for the presence of a unit root in the AR(1) model with a drift:

Yt = beta0 + beta1Yt-1 + ut:

(a) Outline the Dickey-Fuller (ADF) test procedure.

(b) Suppose that we use data on the logarithm of the Gross Domestic Product (GDP), ln(GDP), based on quarterly data from 2000 (Q1) to 2018 (Q4) and we obtain the following OLS estimate : beta^ 0= 0.442, beta^ 1= 0.988, SE( peta^ 0) = 0.12 and SE( beta^ 1) = 0.031 (SE denotes standard error). Does the ln(GDP) appear to be stationary? Justify your answer.Note that the critical values of the DF t-statistic are: -2.57 ( at 10% signicance), -2.87 (at 5% signicance), -3.43 (at 1% signicance)

(c) How does the ADF procedure change if you believe that the error sequence ut is serially correlated?

Answer 1

Take log differences in GDP so y(t) = Ln(Yt)-Ln(Yt-1)

Regress yt= by(t-1) + ut. Test that b = 0. Check for serial correlation in the residuals with DW test (for AR(1)) or something more general looking at the correlogram