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

Author

Listed:
  • Serge Darolles

    (DRM - Dauphine Recherches en Management - Université Paris Dauphine-PSL - PSL - Université Paris Sciences et Lettres - CNRS - Centre National de la Recherche Scientifique)

  • Patrick Duvaut
  • Emmanuelle Jay

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.

Suggested Citation

  • Serge Darolles & Patrick Duvaut & Emmanuelle Jay, 2013. "Least Squares Estimation (LSE) and Kalman Filtering (KF) for Factor Modeling: A Geometrical Perspective," Post-Print hal-01632883, HAL.
    • Handle: RePEc:hal:journl:hal-01632883
    DOI: 10.1002/9781118577387.ch3
    as

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