Newcastle have proved that they can compete favorably with other top flight teams in the English Premier league. The played a 3-3 draw against Manchester City, 0-0 draw with Manchester United. They beat Tottenham 2-1 and won Chelsea 1-0. How else do you want them to prove their ability. Newcastle have one of the best teams currently and the management of the club has the financial power to attract and buy more quality players.
I believe Newcastle even have a better chance of performing better than other top four clubs because they are not competing for any continental trophy which means that their players can just focus on winning the premiership.
Manchester City and Manchester United didn't lose to Newcastle, they only drew. Chelsea and Tottenham are the two teams they managed to overthrow, but not about Arsenal and Liverpool. So I don't think Newcastle have been better, but their form so far has been good.
You can't expect much from Newcastle anyway, so even if they play well and avoid more defeats, there is always a high risk of including them in your betting slip. I know that, and it means they are not believed enough to be able to keep their performance.