The Fundamental Covariance Structure

In this chapter we will lay the foundation for Chapters 3-5. In that regard, our goal is to obtain a complete characterization of the covariance relationship between the innovations and the state vectors. Providing a detailed exposition of this structure is the focus of Section 2.3. First, however, we develop several tools that are needed to prove Lemma 2.4 in Section 2.3 as well as other results in subsequent chapters.