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Orthogonal Projection

In: Multivariate Time Series With Linear State Space Structure

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  • Víctor Gómez

    (Ministerio de Hacienda y Administraciones Públicas Dirección Gral. de Presupuestos, Subdirección Gral. de Análisis y P.E.)

Abstract

In this chapter, the fundamental concepts of orthogonality, best linear predictor, and orthogonal projection for random variables and random vectors are introduced. For a given sequence of random vectors, an algorithm called the innovations algorithm is developed for the orthogonalization of the sequence. State space and VARMA models are introduced and special algorithms to orthogonalize sequences following any of these models are given. Some further topics on orthogonal projection for random vectors are discussed. A first principles approach to the Kalman filter for state space models is described.

Suggested Citation

  • Víctor Gómez, 2016. "Orthogonal Projection," Springer Books, in: Multivariate Time Series With Linear State Space Structure, chapter 0, pages 1-60, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-28599-3_1
    DOI: 10.1007/978-3-319-28599-3_1
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