This thesis discusses the theory and implementation of the Geodetic Data Modelling System (GDMS), a software time series analysis application designed specifically for the analysis of Global Positioning Satellite (GPS), Very Long Baseline Interferometry (VLBI) and Satellite Laser Ranging (SLR) data. The year long project carried out by the authors, involved first prototyping a system in MATLAB, before implementing a full version in ANSI ISO C++. This thesis starts with a brief discussion on the history of time series analysis, and an introduction to the GDMS. It is then further divided into five main chapters, the first of which, provides a comprehensive look at the theory behind all process employed in the system. These include time domain and frequency domain analysis, along with interpolation, windowing and the user interface. The following chapter discusses design methodology, the implementation of the prototype and of the GDMS itself. In addition, issues which arose are examined, along with suggestions for future enhancements that could be made to this system. The fourth chapter discusses the testing methodology, which is an integral part of any systems software design and the fifth chapter discusses the documentation process. The final chapter reflects on the project as a whole in terms of meeting the project team's objectives and expanding their body of knowledge.