Is it possible for someone to accurately predict the future so that what they say will happen does happen when the future becomes the present?
Sure! Within a short temporal distance, most people can predict the future with reasonable accuracy. It's when you want to predict random events or longer time lapse that there's issues. Anyone who can accurately predict random events within a time span of a few hours would already be a multiple lottery winner.
Looking at it like that wouldn't that be more of a prediction based on a chain of events rather than an actual prediction? For instance I can predict the sun will rise tomorrow because I am accustomed to seeing that happen or I know the light will turn green just now because I know in about two minutes it changes. For me that's different than an actual prediction that happens sometime in the future even if its in a short period of time. I know police use prediction based on statistics and habit to form an outcome, it doesn't always work but past experiences makes predictions easier.
Gknightbc and Jolenta make some good points. We can make predictions but its never on something we saw beforehand like those palm readers try to tell us. Its usually on things we believe will happen because on the natural course of things like the sun rising tomorrow *wink*.