The Augmented Dickey-Fuller Test

An Augmented Dickey-Fuller Test (ADF) is a type of statistical test that determines whether a unit root is present in time series data. Unit roots can cause unpredictable results in time series analysis. A null hypothesis is formed on the unit root test to determine how strongly time series data is affected by a trend. By accepting the null hypothesis, we accept the evidence that the time series data is non-stationary. By rejecting the null hypothesis, or accepting the alternative hypothesis, we accept the evidence that the time series data is generated by a stationary process. This process is also known as trend-stationary. Values of the ADF test statistic are negative. Lower values of ADF indicates stronger rejection of the null hypothesis.

Here are some basic autoregression models for use in ADF testing:

• No constant and no trend:

• A...