Hi...When we are dealing with time series data, there might be trend or it may have drift. So, if we will do a model without ignoring for example trend (if actually there is trend in series) then our estimate is Spurious or meaningless. Therefore, we need to change it into stationary by either de-trend or difference. For More details please follow any time series book......
If the variables are stationary at levels, one may use the simple Ordinary Least Square (OLS) regression to examine the long-run relationship between the variables. However, when the variables exhibit mixed order of integration i.e. few independent variables are stationary at levels i.e. I(0) and others are stationary at first difference i.e. I(1), the ARDL bound testing approach proposed by Pesaran et al. (2001) is used to confirm the cointegration among the variables.
Standard tests (i.e. t, F, etc.) are valid when variables are stationary. When variables are not stationary we can not rely on these tests. For easy references start with some undergraduate econometrics books which includes basic time series methods (i.e. Gujarati). You can also look at Enders, Applied Econometric Time Series Methods, as a more advadced reference.