5 - Some Important Processes

Summary

Introduction and Overview

The process of movement from state to state generates a sequence of points on the time axis - the times at which transitions are made. Since movements are probabilistic the passage of a person over time is a realisation of a stochastic, point process. There is a very large literature dealing with the mathematical properties of such processes. Much of this literature deals with the long-run or equilibrium properties when the transition probabilities are constant over time and the process is stationary. In econometrics we usually have to model processes observed over rather short periods of time and which are not stationary, so results from the theory of point processes are not directly relevant. Nevertheless some knowledge of the basic stochastic processes is helpful in thinking about the properties of econometric data as is illustrated by the following example.

Many government statistical services collect and publish information about the duration of unemployment. They obtain this by sampling the population of registered unemployed people and asking them how long they have been unemployed and then they collect the answers in a grouped frequency distribution. Table 5.1 below gives such a distribution for the UK in 1984.