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EdisonCruise
Topic Author
Posts: 97
Joined: September 15th, 2012, 4:22 am

### What makes autoregression different from multiple linear regression？

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.

Alan
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Joined: December 19th, 2001, 4:01 am
Location: California
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### Re: What makes autoregression different from multiple linear regression？

I think the main difference is not in the point estimates of the coefficients, but in their error analysis. With the AR process you often have to consider the issue of unit roots. If present, AFAIK, this invalidates some statistics such as t-stats for assessing if a < 1 in Y(t) = a Y(t-1) + error. Kennedy's 'Guide to Econometrics', esp. Sec 17.5 has some good discussion.

EdisonCruise
Topic Author
Posts: 97
Joined: September 15th, 2012, 4:22 am

### Re: What makes autoregression different from multiple linear regression？

Thank you Alan. But when I use matlab to estimate its VAR model, besides the coefficients in the linear equations, matlab also estimates the covariance matrix as unknowns. In multiple linear regression, there is no covariance matrix or autocorrelation to estimate, because samples are assumed to be indepedent. I guess this maybe the difference.

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