Recursive estimation and residuals

If observations of a regression relationship have a natural ordering, the estimates of the regression parameters based on the first t observations are called recursive estimates. The paper discusses how to obtain these estimates beginning at t = 0 and the relationship of the changes of the estimates to recursive residuals, which are proportional to the differences between the observation of the response variable at time t and its prediction using information up to time t−1. An extension of these ideas to generalized linear models is suggested.