Obstinate, dogged, stubborn, and mulish all mean that someone is unwilling to change course or give up a belief or plan. Obstinate suggests an unreasonable persistence; it's often a negative word.
What connotation is obstinate?
While stubborn may have positive or negative connotations, obstinate is most definitely negative, because it implies a kind of hard-headed determination not to change your mind even when it might be best to rethink your position.
Is it good to be obstinate?
Stubbornness makes us persevere. It helps us stand our ground when everyone else is trying to tell us that we are wrong. Used with discernment, stubbornness can be a strong leadership quality and a key determinant of success. Because stubborn people know what they want, they tend to be more decisive.