Practical Time Series Analysis

Augmented Dickey-Fuller test

The statistical tests for objectively determining whether differencing is required to stationarize a time series are known as unit root tests. There are several such tests of which we discuss the ADF test is one of the unit root tests, that is most commonly used for verifying non-stationarity in the original time series. According to the ADF test, in the presence of autocorrelation, the first-order differences x^'_t of the original series can be expressed as a linear regression model of the previous time index and first-order differences up to a lag of m times indices. The linear regression on x^'_t can be formulated as follows:

In presence of strong autocorrelation, the original series needs differencing and hence ...