Arrival time data from a spatial array of millisecond pulsars can be used (1) to provide a time standard for long time scales, (2) to detect perturbations of the Earth's orbit, and (3) to search for a cosmic background of gravitational radiation. In this paper we first develop a polynomial time series representation for these three effects that is appropriate for analysis of the present data with its limited degrees of freedom. We then describe a pulsar timing array program that we have established at the National Radio Astronomy Observatory 43 m telescope with observations of PSR 1620-26, PSR 1821-24, and PSR 1937+21. The results presented in this paper cover a 2 yr period beginning in 1987 July. Individual parameters of these objects are compared to previous measurements. The influence of global parameters - clock, Earth location, and effects of gravitational radiation - on our data is discussed in the context of our polynomial model. Improvements in the data-gathering hardware and the inclusion of data from other observatories will lead to a significant increase in the sensitivity of this effort in the near future.