Linear Models and Time-Series Analysis

4The AR(1) Model

The auto‐regressive assumption is often justified by the argument that omitted variables are subject to an auto‐regressive process. This argument holds, however, only if all omitted factors contributing to the additive disturbance are subject to auto‐regressive processes with the same parameter. The widespread use of the auto‐regressive correction in econometrics is explained by the fact that it accounts for serial correlation and is computationally efficient. The adaptive regression also explains serial correlation, is computationally efficient, and assumes an error structure which, in many situations, provides a better approximation of reality.

(Thomas F. Cooley and Edward C. Prescott, 1973, p. 364)

In essentially all complex systems, whether in biology, economics, finance, medicine, meteorology, political science, sociology, etc., the actual mechanism that gives rise to the observed data is highly complicated and quite possibly changing over time. Moreover, it often involves a large number of (possibly interacting) factors, many of which will be difficult to measure and/or properly account for in a succinct model. As a result, it is of value to find simple approximations to reality that nevertheless capture some of the primary aspects of the process under study. This is the notion addressed in the above quote by Cooley and Prescott (1973 ), and for which allowing time‐varying parameters might offer a better solution, as discussed in Section 5.6.

In this and ...