Programming the statistical procedures from SAS

Breusch Pagan Incorrect Degrees of Freedom

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Breusch Pagan Incorrect Degrees of Freedom

I am trying to calculate the Breusch Pagan test statistic on a model with autoregressive errors that is estimated using the Cochrane Orcutt method. I also want to calculate the test statistic using whitened data. In order to calculate the statistic I run proc model with the BREUSCH option. However, I am getting an incorrect number of degrees of freedom. There are 3 parameters in the model therefore, there should be 3 DoF in calculating the p-value for the BP statistic; however, SAS is saying there is 1 DoF. Do you know how SAS calculates the degrees of freedom? Also SAS is including the intercept and AR terms in the models degree of freedom, is there a way to not include those?

 

Here is the SAS code that I have:

proc model data = model_data_estimation;
parms intercept 0 b1 0 b2 0 b3 0 rho1 0 rho2 0 rho3 0 rho4 0;
yhat = intercept + b1 * x1 + b2 * x2 + b3 * x3;
y = intercept + b1 * x1 + b2 * x2 + b3 * x3 - (rho1*LAG1(yhat-y)) - (rho2*LAG2(yhat-y)) - (rho3*LAG3(yhat-y)) - (rho4*LAG4(yhat-y));
whitened_x1 = x1 - (rho1 * LAG(x1)) - (rho2 * LAG2(x1)) - (rho3 * LAG3(x1)) - (rho4 * LAG4(x1));
whitened_x2 = x2 - (rho1 * LAG(x2)) - (rho2 * LAG2(x2)) - (rho3 * LAG3(x2)) - (rho4 * LAG4(x2));
whitened_x3 = x3 - (rho1 * LAG(x3)) - (rho2 * LAG2(x3)) - (rho3 * LAG3(x3)) - (rho4 * LAG4(x3));
fit y / white BREUSCH=(whitened_x1 whitened_x2 whitened_x3);
run;

Here is the output of the code:

Nonlinear OLS Summary of Residual Errors

Equation

DF Model

DF Error

SSE

MSE

Root MSE

R-Square

Adj R-Sq

y

8

103

0.00726

0.000071

0.00840

0.8154

0.8028

 

 

Nonlinear OLS Parameter Estimates

Parameter

Estimate

Approx Std Err

t Value

Approx
Pr > |t|

intercept

0.009013

0.00146

6.16

<.0001

b1

0.133953

0.00707

18.94

<.0001

b2

0.014151

0.00236

6.01

<.0001

b3

1.531773

0.4791

3.20

0.0018

rho1

0.47984

0.0909

5.28

<.0001

rho2

0.053752

0.1000

0.54

0.5922

rho3

0.154562

0.1003

1.54

0.1265

rho4

-0.41136

0.0895

-4.60

<.0001

 

 

Number of Observations

Statistics for System

Used

111

Objective

0.0000654

Missing

0

Objective*N

0.007263

 

 

Heteroscedasticity Test

Equation

Test

Statistic

DF

Pr > ChiSq

Variables

y

White's Test

71.46

15

<.0001

Cross of all vars

 

Breusch-Pagan

3.59

1

0.0581

whitened_x1, whitened_x2, whitened_x3, 1

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