Linear difference equations
In the study of many problems, the change in a variable is most naturally modeled
in discrete units of time. For many bank loans, interest is computed on a monthly
basis so that the level of debt is updated on a monthly basis. Government data
are routinely released on a quarterly or annual basis, firms report profit each
quarter. Thus, unemployment data or profit data are seen as sequences ut,ut−1, . . .
or pit,pit−1, . . .. When the data evolve according to a systematic pattern, difference
equations may be used to study long-run behavior.