Yes unit root testing is nonstationarity testing. The null hypothesis is a statement of the existence of a unit root which implies nonstationarity. Forecasting a non stationary series is unreliable hence the need for the test. If the test is nonsignificant, there will be need to difference the series. To the original series an ARIMA model may be fitted.

Yes, ARMA model should be applied to stationary data. Moreover, if WPI is wholesale price index, then you should study percentage changes in this index, not index itself.

Thank you all. I have applied unit root testing for 1st difference of the data series and found no unit root. Therefore no issue to proceed.

If WPI is a wholesale price index you should probably be working with the log of the series. An ARMA(4,4) model is very over specified for such a series and you should be using a more parsimonious model. It is possible that the ARMA(4,4) model is due to the use of levels rather than the log of the series.

PMC Thakshila says "I have applied unit root testing for 1st difference of the data series and found no unit root.". This means that ARMA modelling is OK for the first differences of WPI, not for the levels of WPI. Applying ARMA(p,q) to first differences is the same as applying ARIMA(p,1,q) to the levels.

Thank you John C Frain. Thank you Vince Daly so much for the clearance. I mentioned that on my second question. I applied unit root testing according to the expert comments for my time series data.

The unit root test is necessary because if your series contains a unit root then the ARMA model applied on a series in level causes imprecise predictions. Most often the time series have a unit root and it is the strategy of Box and Jenkins that will show you the order AR and MA after of course that you use a difference variable first and not level