ADF & Order of Integration

Question 1

What ADF test?

Answer 1

The Augmented Dickey-Fuller test is used to check whether a time series is stationary or has a unit root (non-stationary)

Question 2

What are the null and alternative hypotheses in the ADF test?

Answer 2

H0: γ = 0 (unit root)

H1: γ < 0 (stationary)

Question 3

What is the test equation for the ADF test?

Answer 3

ΔYt = a + γYt-1 + ∑δi ΔYt-i + ut

​ΔYt = First difference of the series

𝛾 = The key coefficient - testing whether its 0

∑δi ΔYt-i =Lagged differences to fix autocorrelation

Question 4

What does I(1) mean?

Answer 4

The series becomes stationary after 1 difference

Question 5

What table should you use to interpret the ADF test statistic?

Answer 5

Dickey-Fuller critical value table (not standard t-table)

Question 6

Stationary series I(0)

Answer 6

A time series with constant mean, variance, and autocovariance

Question 7

When should you take first differences?

Answer 7

When the series is non-stationary (e.g. has a unit root) and is 𝐼(1)

Question 8

Why are lagged differences included in the ADF test?

Answer 8

To control for autocorrelation and ensure the error term is white noise.

Question 9

What are the null and alternative hypotheses of the Dickey-Fuller test?

Answer 9

H0​:ρ=1 (unit root),
​
H1:∣ρ∣<1 (stationary)