Time Series Models for Count or Qualitative Observations
Andrew C. Harvey, C Fernandes · 2005
Abstract It is not unusual to find time series consisting of count data. Such series record the number of events occurring in a given interval and are necessarily nonnegative integers. An example would be the number of accidents occurring in a given period. The number of goals scored by England against Scotland in international football matches also has the characteristics of count data. Count data models are usually based on distributions such as the Poisson or negative binomial. If the means of these distributions are constant or can be modeled in terms of observable variables, then estimation is relatively easy; see, for example, the book on generalized linear models (GLIM) by McCullagh and Nelder (1983). The essence of time series models, however, is that the mean of a series cannot be modeled in terms of observable variables but depends on some stochastic mechanism.