Chapter 18 Dynamic specification

Dynamic specification denotes the problem of appropriately matching the lag reactions of a postulated theoretical model to the autocorrelation structure of the associated observed time-series data. As such, the issue is inseparable from that of stochastic specification if the finally chosen model is to have a purely random error process as its basic innovation. The subject-matter has advanced rapidly and offers an opportunity for critically examining the main themes and integrating previously disparate developments. A statistical-theory based model considers the joint density of the observables and seeks to characterize the processes whereby the data were generated. Thus, the focus is on means of simplifying the analysis to allow valid inference from submodels. This chapter also discusses that given the paucity of dynamic theory and the small sample sizes currently available for most time series of interest, as against the manifest complexity of the data processes, all sources of information have to be utilized. Attempt to resolve the issue of dynamic specification first involves developing the relevant concepts, models, and methods that is the deductive aspect of statistical analysis, prior to formulating inference techniques. An alternative interpretation is that by emphasizing the econometric aspect of time-series modeling, the analysis applies howsoever the model is obtained and seeks to be relatively neutral as to the economic theory content.