Deterministic properties of serially connected distributed lag models

Distributed lag models are an important tool in modeling dynamic systems in economics. In the analysis of composite forms of such models, the component models are ordered in parallel (with the same independent variable) and/or in series (where the independent variable is also the dependent variable in the preceding model). This paper presents an analysis of certain deterministic properties of composite distributed lag models composed of component distributed lag models arranged in sequence, and their asymptotic properties in particular. The models considered are in discrete form. Even though the paper focuses on deterministic properties of distributed lag models, the derivations are based on analytical tools commonly used in probability theory, such as probability distributions and the central limit theorem.