When doing cointegration tests should I use the adjusted close price or just close price for the time series? The dividend of each stock is on different dates and can cause jumps in the data.
Such tests should always be done using adjusted prices. In fact, ideally, you should reconstruct your own price series using the total returns series. To see this, suppose you have a 10:1 split rather than a relatively small cash dividend. Then it is clear that the cointegration relationship can only hold with respect to the adjusted series.