For an AR(2) process Yt=a1*Yt-1+a2*Yt-2+b, is it different from Y=a1*X1+a2*X2+b, where X1 and X2 can be replaced by Yt-1 and Yt-2 respectively? As I know, the estimation of both models can use least square method and some book state’We can therefore state that in the case of VAR processes, the LS estimators are the same as the OLS estimators computed equation by equation.’ (Financial modeling of the Equity Market, FRANK J. FABOZZI). AS I know, AR or VAR takes autocorrelation into consideration, but it seems that AR and VAR just take Yt-1 and Yt-2 as independent variables and there is no special treatment to autocorrelation in the model estimation process. So I am a bit confused on the difference between autoregression and multiple linear regression.
Any suggestion is appreciated.