Monitored network data allows operators to gain valuable insight into the health and status of a network. Whilst such data is useful for real-time analysis, there is often a need to post-process historical network performance data. Storage of the monitored data then becomes a serious issue as network monitoring activities generate significant quantities of data. The work in this thesis is motivated by the need of measuring the performance of high-speed networks. Such networks produce large amounts of data over a long period of time, making the storage of this information practically inefficient. A possible solution to this problem is to use lossy compression on an on-line system that intelligently compresses computer network measurements while preserving the quality in important characteristics of the signal. This thesis contributes to the knowledge by examining two threshold estimation techniques, two threshold application techniques and the impact of window size on the lossy compression performance. In addition eight different wavelets were examined in terms of compression performance, energy preservation, scaling behaviour, quality attributes and Long Range Dependence.