Unit root indicates a stochastic trend in the time series. Sometimes it is known as “random walk with drift”. A time series dataset will show a systematic unpredictable pattern if it has the unit root. If a time series dataset has the unit root, the regression result will be unreasonable and provide a spurious result (in which there is large r-squared value even if the data is uncorrelated) and errant behavior (in which t-rations will not follow at- distributions). Therefore it is important to perform unit root test.
Problems with unit root
Presence of unit root also causes that series to be non-stationary. A series should be stationary where its statistical properties do not vary with time (expectation, variance, autocorrelation). Stationary data will give better results. The main problems associated with unit roots are:
- The variance will not be constant
- Ordinary Least Square (OLS) estimates will be biased.
Therefore, it becomes necessary to perform unit root test and correct unit root.
Using an augmented dickey-fuller test for checking the unit root
In case of serial autocorrelation, Augmented Dickey-Fuller (ADF) test is used to examine the presence of unit root. The null hypothesis for the ADF test is that there is a unit root (means series is non-stationary). Then differencing of the variable is used to make a stationary series (not autocorrelated). The alternative hypotheses are that there is no presence of unit root.
For instance, in the FDI study, the data on FDI is coming out to be non-stationary, which implies that its series do not have a constant mean, constant variance, and constant co-variance over time. Therefore the ADF test was applied to the correct unit root.