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He told the Hull Daily Mail: "After the start we've had, you don't just overcome it with a couple of wins.
"It takes two or three months to rectify the start we've had and it could be Christmas before we come out of this, but we will come out of it."
On Saturday, Parkinson comes up against his predecessor Taylor, who is now in charge of Crystal Palace after leaving Hull City with two promotions to his name.
Pearson says he understands the difficulty Parkinson faces in following that.
"You go into a club that has been moulded by another manager and it's a very difficult job.
"The new person coming in needs to be given a lot of time. If you don't give that manager time, everything goes back to the drawing board.
"That is not going to happen at this football club and Phil is going to be given as much time as he needs to make his mark on the team.
"If it takes until the summer, he will be given all the time he needs."
He also said that even if the fans lose faith in Parkinson's ability to turn things around, Pearson will still keep faith in the former Colchester boss because of his "integrity, commitment, hard work and ability."