Augmented Dickey-Fuller Test

Augmented Dickey-Fuller test is a unit root test of whether a time series is non-stationary, regressing the differenced series on its lagged level and lagged differences to absorb serial correlation.

확장 디키-풀러 검정은 차분한 계열을 직전 수준값과 시차 차분항에 회귀시켜 시계열에 단위근, 즉 비정상성이 있는지를 검정하는 단위근 검정이다.

How do I test whether my time series is stationary or needs differencing before modelling?

시계열이 정상적인지, 모형을 세우기 전에 차분이 필요한지 어떻게 검정하나요?

The augmented Dickey-Fuller test takes a unit root, meaning non-stationarity, as its null hypothesis, so a significant result supports stationarity. It adds lagged differences to the test regression to handle autocorrelation, and it is often paired with the KPSS test, whose null hypothesis is the reverse.

When to use Augmented Dickey-Fuller Test

• Deciding whether to difference a series before ARIMA modelling
• Checking for a unit root before cointegration or VAR analysis
• A single, regularly spaced time series of reasonable length

When to use something else

• Series with a clear deterministic trend, which this constant-only version does not model: use an ADF or KPSS test that includes a trend term
• Many short series observed in parallel: use a panel unit root test

Assumptions and requirements

• Regularly spaced observations ordered by time
• Test regression with a constant but no linear trend
• Lag length chosen by AIC is enough to remove residual autocorrelation

What the analysis reports

• ADF statistic
• MacKinnon approximate p-value
• Number of lagged differences selected
• 5% critical value
• Warning to difference the series when a unit root is not rejected

How to report it

An augmented Dickey-Fuller test rejected the null hypothesis of a unit root for [series], ADF = [value], p = [value], with [value] lags selected by AIC.

Related methods

• KPSS Test
• ARIMA Model
• Panel Unit Root Test

Run Augmented Dickey-Fuller Test on Quorant