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Proc Autoreg : Chow test on single variable

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Proc Autoreg : Chow test on single variable

Hi All, I have below code:- proc autoreg data=Data; model x=/chow=80; run; In this how does F value for Chow test gets computed as only one variable is provided. How would two seperate regression be computed for breakpoint 80. Please help me understand how does Chow test in this case works. Thanks

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3 weeks ago
SAS Employee
Posts: 2

Re: Proc Autoreg : Chow test on single variable

The model you specififed is an intercept only model where the only parameter is the intercept. It is just a special case of a regression model with both intercept and slope parameter. And the computation of Chow test follows the same formula. You split the sample into two subsamples, the first one contains observations from 1 to 79, the second subsample contains observations from 80 and above, and you perform the same regression(intercept only regression) on each of the two subsamples. Instead of testing both the intercept and slope parameter(in the case when you have an independent variable and intercept) are different across the two subsamples, you are now testing(in the case of intercept only model) that the intercept parameter is different in the two subsamples. You can use the formula for Chow test in the documentation to compute the Chow test after spliting the samples:

 

\[ \mr{F}_\mi {chow} = \frac{({\mb{\hat{u}} ’}\mb{\hat{u}} - {\mb{\hat{u}}’}_{1}\mb{\hat{u}} _{1} - {\mb{\hat{u}}’}_{2}\mb{\hat{u}} _{2}) / {k}}{( {\mb{\hat{u}}’}_{1} \mb{\hat{u}} _{1} + {\mb{\hat{u}}’}_{2} \mb{\hat{u}} _{2}) / (n_{1}+n_{2}-2k)} \]

 

where ${\mb{\hat{u}} }$ is the regression residual vector from the full set model, ${\mb{\hat{u}} _{1}}$ is the regression residual vector from the first set model, and ${\mb{\hat{u}} _{2}}$ is the regression residual vector from the second set model, n1 and n2 are the numbers of observations in each of the two subsamples, and k is the number of parameters which is equal to 1 in the case with intercept only model.

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Solution
3 weeks ago
SAS Employee
Posts: 2

Re: Proc Autoreg : Chow test on single variable

The model you specififed is an intercept only model where the only parameter is the intercept. It is just a special case of a regression model with both intercept and slope parameter. And the computation of Chow test follows the same formula. You split the sample into two subsamples, the first one contains observations from 1 to 79, the second subsample contains observations from 80 and above, and you perform the same regression(intercept only regression) on each of the two subsamples. Instead of testing both the intercept and slope parameter(in the case when you have an independent variable and intercept) are different across the two subsamples, you are now testing(in the case of intercept only model) that the intercept parameter is different in the two subsamples. You can use the formula for Chow test in the documentation to compute the Chow test after spliting the samples:

 

\[ \mr{F}_\mi {chow} = \frac{({\mb{\hat{u}} ’}\mb{\hat{u}} - {\mb{\hat{u}}’}_{1}\mb{\hat{u}} _{1} - {\mb{\hat{u}}’}_{2}\mb{\hat{u}} _{2}) / {k}}{( {\mb{\hat{u}}’}_{1} \mb{\hat{u}} _{1} + {\mb{\hat{u}}’}_{2} \mb{\hat{u}} _{2}) / (n_{1}+n_{2}-2k)} \]

 

where ${\mb{\hat{u}} }$ is the regression residual vector from the full set model, ${\mb{\hat{u}} _{1}}$ is the regression residual vector from the first set model, and ${\mb{\hat{u}} _{2}}$ is the regression residual vector from the second set model, n1 and n2 are the numbers of observations in each of the two subsamples, and k is the number of parameters which is equal to 1 in the case with intercept only model.

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