Partial autocorrelation function: Difference between revisions

Revision as of 01:54, 12 October 2019

Revision as of 02:01, 12 October 2019

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: <math>\alpha(1) = \operatorname{corr}(z_{t+1}, z_{t}),\text{ for }k= 1,</math>

: <math>\alpha(k) = \operatorname{corr}(z_{t+k+1} - P_{t,k}(z_{t+k+1}),\, z_{t+1} - P_{t,k}(z_{t+1})),\text{ for }k\geq 2,</math>

where <math>P_{t,k}(x)</math> is surjective operator of orthogonal projection of <math>x</math> onto the linear subspace of Hilbert space spanned by <math> x_{t+1}, \dots, x_{t+k}</math>.