# Does Auto-correlation cause AR(p) model?

This is the autocorrelation case.

$y_{t}=X_{t}B+u_{t}$

where $u_{t}=\rho u_{t-1}+e_{t},$ $e_{t}$ is iid

From this autocorrelated disturbances,

I might be able to say

$y_{t}=\gamma y_{t-1}+w_{t}$, i.e., ordinal AR(1) model

Is this right?

Yes ....

If you have

yt=XtB+ut where ut=ρut−1+et, et is iid

and you clear fractions then you have a model of the form

y(t)= γy(t−1) + X_{t}-[1-γ]X_{t-1} + e_t$, and$e_t$is iid. where$w_t= X_{t}-[1-γ]X_{t-1} + e_t$, and$e_t\$ is iid.

• This is being automatically flagged as low quality, probably because it is so short. Could you expand it a little? – gung - Reinstate Monica Dec 3 '15 at 14:43
• This does not look like an AR(1) model to me; should it? – Richard Hardy Dec 3 '15 at 18:07
• No ....it should not – IrishStat Dec 3 '15 at 21:00
• So why is your answer a "yes"? – Richard Hardy Dec 3 '15 at 22:20
• YES if you consider w(t) to be not iid – IrishStat Dec 3 '15 at 23:30