ADF & Order of Integration Flashcards
What ADF test?
The Augmented Dickey-Fuller test is used to check whether a time series is stationary or has a unit root (non-stationary)
What are the null and alternative hypotheses in the ADF test?
H0: γ = 0 (unit root)
H1: γ < 0 (stationary)
What is the test equation for the ADF test?
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
What does I(1) mean?
The series becomes stationary after 1 difference
What table should you use to interpret the ADF test statistic?
Dickey-Fuller critical value table (not standard t-table)
Stationary series I(0)
A time series with constant mean, variance, and autocovariance
When should you take first differences?
When the series is non-stationary (e.g. has a unit root) and is 𝐼(1)
Why are lagged differences included in the ADF test?
To control for autocorrelation and ensure the error term is white noise.