In Chapter 1 we discussed the distinction between strongly and weakly restricted time series models. A weakly restricted model uses techniques such as those we studied in Chapter 2, where one primarily infers from the data the structure of the data-generating process by assessing the AR and MA components of an observed univariate series. Extending the weakly restricted approach to multivariate models, which we do in subsequent chapters, leads to the use of vector autoregression (VAR) and error correction models (ECMs). Important modeling choices, such as how many lags of a variable to include, are inferred from the data rather than specified before the analysis. Recall as well that the quasi-experimental approach uses weakly restricted models, highlighting the problem of specification uncertainty.
In this chapter we discuss strongly restricted time series modeling, which assumes that we know much more about the functional forms of our data-generating process. Making these strong assumptions about a time series' functional form and proceeding directly to testing hypotheses about the relation-ships between variables encompass what we term the “time series regression tradition.” This approach is popular and widely used. It is appropriate whenever an analyst can comfortably and ably make the strong assumptions required for the technique.
We provide an overview of the basic components of time series regression models and explore tests for serial correlation in the residuals, which provide guidance to analysts regarding various types of serial correlation.