This research is to attack the thorny problem of analyzing data that comes from measurements made, or observed, repeatedly but not regularly over time. A novel approach using successive differences is proposed as the basis for analysis assuming piece- wise linearity in the interval of varying lengths. The question to be studied is how to decide where to subdivide the time interval. The traditional methods for analyzing data which is collected repeatedly over time were developed to answer questions posed by the financial community. Financial data is not missing and can be collected at regular fixed time intervals. Because of the structure available in the data driving the early developments in this subfield, the assumptions of a fixed and rigid data structure is built into these analytic approaches. In many fields of research, however, data cannot be collected according to a fixed time schedule as can be done when measuring dollars and cents. Radically new methods of analysis are needed to obtain valid tools for such data, in as much as conclusions are being drawn and decisions based on results from very ad hoc analytical procedures. This research aims to work toward a statistical theory that will be valid for this general framework of scientific investigation.
