Derivation of the Partial Autocorrelation Function (PACF), specifically \( \phi_{22} \), for an AR(2) Model

Students often confuse \

\\phi_{kk} \

with \

\\rho_k \

or the \

k^{th} \

coefficient of an AR(p) process where \

p \

is not \

k \

. \

\\phi_{kk} \

is *specifically* the last coefficient of an AR(k) process fitted to the data, not just any \

\\phi_k \

Institutional Reference: Time Series Analysis