Partial autocorrelation function: Difference between revisions

Revision as of 11:16, 5 March 2019

Revision as of 11:19, 5 March 2019

Line 11:

: <math>\alpha(1) = \operatorname{Cor}(z_{2}, z_1),\text{ for }k= 1,</math>

: <math>\alpha(k) = \operatorname{Cor}(z_{t+k} - P_{t,k}(z_{t+k}),\, z_t - P_{t,k}(z_tz_{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-1}</math>.