DickeyFullerTest

The DickeyFullertest, also known as the Dickey-Fuller test or Augmented Dickey-Fuller (ADF) test, is a statistical test used in time series analysis to determine if a time series is stationary. A stationary time series is one whose statistical properties, such as mean, variance, and autocorrelation, do not change over time. Non-stationary time series can lead to spurious regression results, making it crucial to identify and address them.

The ADF test works by testing the null hypothesis that a unit root is present in a time series. The presence of a unit root implies that the time series is non-stationary. If the null hypothesis is rejected, it suggests that the time series is stationary. The test includes lagged difference terms and a constant or trend to account for serial correlation in the error terms, making it "augmented" compared to the original Dickey-Fuller test.

The test statistic is compared to critical values, and if the test statistic is more negative than the critical value, the null hypothesis of a unit root is rejected, indicating stationarity. The ADF test is widely used in econometrics and finance to pre-process data before applying various time series models, such as ARIMA. It is important to note that the ADF test has limitations and can sometimes be sensitive to the number of lags included and the presence of structural breaks in the data.