Least Squares Estimation (LSE) and Kalman Filtering (KF) for Factor Modeling: A Geometrical Perspective

Serge Darolles, Patrick Duvaut and Emmanuelle Jay

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Abstract: This chapter introduces, illustrates and derives both least squares estimation (LSE) and Kalman filter (KF) estimation of the alpha and betas of a return, for a given number of factors that have already been selected. It formalizes the "per return factor model" and the concept of recursive estimate of the alpha and betas. The chapter explains the setup, objective, criterion, interpretation, and derivations of LSE. The setup, main properties, objective, interpretation, practice, and geometrical derivation of KF are also discussed. The chapter also explains the working of LSE and KF. Numerous simulation results are displayed and commented throughout the chapter to illustrate the behaviors, performance and limitations of LSE and KF.

Keywords: geometrical interpretation; Kalman filtering (KF); least squares estimation (LSE); per return factor model (search for similar items in EconPapers)
Date: 2013
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Published in Multi-factor models and signal processing techniques: application to quantitative finance, pp.59-116, 2013, ⟨10.1002/9781118577387.ch3⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-01632883

DOI: 10.1002/9781118577387.ch3

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