I'm fairly sure that the short answer is no. Time cannot be defined as absolute, only relative to one point or another. So "time itself" is not slower at one position, unless defined relative to another position.
No, time in space is faster than on Earth unless you are traveling near the speed of light. As you approach a massive object such as a planet time slows down as you get closer to the planet. The more massive the object the slower time flows near it. A black hole is a good example of this effect on time. As you get closer to a black hole time begins to slow down until you reach the area called the "event horizon" where time stops. Another example of this effect from a different perspective, the GPS satellites moving around Earth experience a faster flow of time than we do on Earth because they are further away from the curvature of space created by the mass of the Earth. This effect of time on the satellites are corrected by an onboard program on each satellite before the signal from them are sent to GPS devices on the Earth's surface. This corrected signal is how GPS devices determine our position correctly on the surface. Furthermore, if this signal was not corrected; all the GPS devices on the surface would be giving us the wrong position because of this difference in time flow on the satellites versus the time flow on the Earth's surface.
Time does move slower in space but only to the outside observer. This is due to the effects of Time Dilation (see http://nishlaverz.hubpages.com/hub/Time-Dilation.)
However the idea of time running slower in space is contradicted by gravitational time dilation. This shows that time runs slower the closer to a gravity source you are. So a clock on the ground should run slower than on suspended in the air. See link above.
It is a confusing subject as you have to look at all the different forms of time dilation and factor in all the objects and velocities travelled to get the answer.
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