Orthogonal Projection

Víctor Gómez
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Víctor Gómez: Ministerio de Hacienda y Administraciones Públicas Dirección Gral. de Presupuestos, Subdirección Gral. de Análisis y P.E.

Chapter Chapter 1 in Multivariate Time Series With Linear State Space Structure, 2016, pp 1-60 from Springer

Abstract: 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.

Keywords: Mean Square Error; Kalman Filter; Random Vector; Orthogonal Projection; Covariance Matrice (search for similar items in EconPapers)
Date: 2016
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-28599-3_1

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DOI: 10.1007/978-3-319-28599-3_1

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