In this book, I highlight the developments in Kalman filtering subject to general linear constraints. Essentially, the material to be presented is almost entirely based on the results and examples originally developed in Pizzinga et al. (2008a), Cerqueira et al. (2009), Pizzinga (2009, 2010), Souza et al. (2011), Pizzinga et al. (2011), and Pizzinga (2012). There are fundamentally three kinds of topics: (a) new proofs for already established results within the restricted Kalman filtering literature; (b) additional results that are should shed light on theoretical and methodological frameworks for linear state space modeling under linear restrictions; and (c) applications in investment analysis and in macroeconomics, where the proposed methods are illustrated and evaluated. At the end, I briefly discuss some extensions in the subject, which, again, step into theory, methods, and applications.
In statistics, the Kalman filter is a mathematical method whose purpose is to use a series of measurements observed over time, containing random variations and other inaccuracies, and produce estimates that tend to be closer to the true unknown values than those that would be based on a single measurement alone. This Brief offers developments on Kalman filtering subject to general linear constraints. There are essentially three types of contributions: new proofs for results already established; new results within the subject; and applications in investment analysis and macroeconomics, where the proposed methods are illustrated and evaluated. The Brief has a short chapter on linear state space models and the Kalman filter, aiming to make the book self-contained and to give a quick reference to the reader (notation and terminology). The prerequisites would be a contact with time series analysis in the level of Hamilton (1994) or Brockwell & Davis (2002) and also with linear state models and the Kalman filter – each of these books has a chapter entirely dedicated to the subject. The book is intended for graduate students, researchers and practitioners in statistics (specifically: time series analysis and econometrics).