p=0 is a statement for the null hypothesis that assumes that the error term in one period is not correlated to the error term in the previous period.
The Durbin-Watson test is used in regression analysis to test for autocorrelation. The results from the test would always range from 0 to 4. A value of less than 2.0 indicates positive autocorrelation. A value of 2.0 indicates no autocorrelation, and a value of 2.0 to 4.0 indicates negative autocorrelation.