Cochorane-Orcutt procedure

[cuongnh]

Dear Startz, hello again. I come back to you with a same question before that relates to CO. I am using CO to correct serial correlation, but after the first step of using CO, which range of data, the original or the ones got after the first step CO, I should use with rho to make a new range of data for use of the second step of CO. Please help me!

[startz]

Dear Startz, hello again. I come back to you with a same question before that relates to CO. I am using CO to correct serial correlation, but after the first step of using CO, which range of data, the original or the ones got after the first step CO, I should use with rho to make a new range of data for use of the second step of CO. Please help me!

I'm not sure exactly what you mean, as the data never changes.

Why not use the built-in AR(1) procedure?

[cuongnh]

Thanks Startz for your reply.
I think I am still very far away from well understanding the C-O procedure. What I have ask you is that I am using C-O to transform the equation by using rho obtained from residuals. Let me explain you a bit more carefully:
My first equation is that "priceofrice c priceofoil dummy1 dummy2 dummy3" (as in Eviews),
I got residuals from the regression of the above model, then calculated rho from those residuals
I used that rho in calculating NEW priceofrice, priceofoil dummy1, dummy2, dummy3 with following methods:
for the first observations, I used method of Prais-Winsten: Y1*(1–(p)^2 )^0.5 and X1*(1–(p)^2)^0.5 (p is rho)
for the second observation and upwards. I used the method: new priceofrice = priceofrice – ppriceofrice_t–1, and same application to all independent variables,
I regressed again with NEW data of priceofrice, priceofoil, dummy1, dummy2, dummy3 (this is so called step 1)
And I got NEW residuals for calculating NEW rho.
I want to do repeatly this procedure, but my question is that: If I want to repeat one more time the procedure, means that I have to use NEW rho to calculate NEW data for dependent and independent variables, but I dont know whether I have to use rho with original data (the ones I used in the very beginning regression) or with NEW data as I called above in Step 1?
Below is the data in excel sheet: e.g. price means price of rice, and price1 means price of rice after one step of using rho to calculate new data. I want to do one more step to get price3, but in order to do that i need rho (can be obtained from regression of price1...) and I dont know i should use that rho with data in price or price1 to get price2:
PRICE POIL DRICQ RTDRICQ st sst DVXB SDVXB DTHS PRICE1 POIL1 RTDRICQ1 sst1 SDVXB1 DTHS1
10.94 71.65 1.00 1.00 0.00 0.00 0.00 0.00 0.00 5.96 39.02 0.54 0.00 0.00 0.00
10.83 71.94 1.00 1.00 0.00 0.00 0.00 0.00 0.00 1.65 11.85 0.16 0.00 0.00 0.00
10.91 72.06 1.00 1.00 0.00 0.00 0.00 0.00 0.00 1.83 11.72 0.16 0.00 0.00 0.00
10.90 72.60 1.00 1.00 0.00 0.00 0.00 0.00 0.00 1.75 12.16 0.16 0.00 0.00 0.00
10.89 72.49 1.00 1.00 0.00 0.00 0.00 0.00 0.00 1.74 11.60 0.16 0.00 0.00 0.00
10.72 73.00 1.00 1.00 0.00 0.00 0.00 0.00 0.00 1.59 12.20 0.16 0.00 0.00 0.00
10.67 72.67 1.00 1.00 0.00 0.00 0.00 0.00 0.00 1.68 11.44 0.16 0.00 0.00 0.00
10.81 72.54 1.00 1.00 0.00 0.00 0.00 0.00 0.00 1.86 11.59 0.16 0.00 0.00 0.00

I am sorry if these explanation are still unclear to you.
And further more, could you please explain me more carefully about using AR(1) procedure instead of doing repeatly C-O.
Thank you very much!

[startz]

Thanks Startz for your reply.
I think I am still very far away from well understanding the C-O procedure. What I have ask you is that I am using C-O to transform the equation by using rho obtained from residuals. Let me explain you a bit more carefully:
My first equation is that "priceofrice c priceofoil dummy1 dummy2 dummy3" (as in Eviews),
I got residuals from the regression of the above model, then calculated rho from those residuals
I used that rho in calculating NEW priceofrice, priceofoil dummy1, dummy2, dummy3 with following methods:
for the first observations, I used method of Prais-Winsten: Y1*(1–(p)^2 )^0.5 and X1*(1–(p)^2)^0.5 (p is rho)
for the second observation and upwards. I used the method: new priceofrice = priceofrice – ppriceofrice_t–1, and same application to all independent variables,
I regressed again with NEW data of priceofrice, priceofoil, dummy1, dummy2, dummy3 (this is so called step 1)
And I got NEW residuals for calculating NEW rho.
I want to do repeatly this procedure, but my question is that: If I want to repeat one more time the procedure, means that I have to use NEW rho to calculate NEW data for dependent and independent variables, but I dont know whether I have to use rho with original data (the ones I used in the very beginning regression) or with NEW data as I called above in Step 1?

I am sorry if these explanation are still unclear to you.
And further more, could you please explain me more carefully about using AR(1) procedure instead of doing repeatly C-O.
Thank you very much!

First thing is, you've left out the rho when you calculate your new variables.
But the easy way to do this is

Code: Select all

ls priceofrice c priceofoil dummy1 dummy2 dummy3 ar(1)

[cuongnh]

Dear Startz, I did used rho when calculating new variables. What do you mean by saying "left out rho"?

[startz]

You wrote

I used the method: new priceofrice = priceofrice – ppriceofrice_t–1, and same application to all independent variables

No rho. (Maybe it was a typo?)

[cuongnh]

You wrote

I used the method: new priceofrice = priceofrice – ppriceofrice_t–1, and same application to all independent variables

No rho. (Maybe it was a typo?)

In this: new priceofrice = priceofrice – ppriceofrice_t–1, ppriceofrice_t-1 means rho (symboled by p)*priceofrice_t-1. Is that right?

[cuongnh]

Dear Startz, I have just found one thing interesting. Before, when I calculate rho manually from residuals, I always missed one first value in the column of e_t*e_t-1. It means that if the total number of observations is 20, I have only 19 values of e_t*e_t-1 and 20 values of e_t^2. But, this time I just take the first residual to include as first value of e_t*e_t-1, then sum up e_t*e_t-1 and also sum up e_t^, then divide sum of e_t*e_t-1 by e_t^2, the result is exactly the same as value of ar(1) if i include in the equation. Below is example of the calculation of rho. The bold value is taken from first residual as the first value of e_t*e_t-1:
Residuals e_t*e_t-1 e_t^2
5.635782 5.635782 31.76203875
1.139445 6.421663621 1.298334908
-0.384953 -0.438632771 0.148188812
2.187106 -0.841933016 4.783432655
-0.526497 -1.151504748 0.277199091
-6.177807 3.252596852 38.16529933
-5.715309 35.30807595 32.66475697
0.964245 -5.510958127 0.92976842
5.077202 4.895666642 25.77798015
0.325358 1.651908288 0.105857828
-0.597564 -0.194422228 0.357082734
-2.650145 1.583631247 7.023268521
1.590108 -4.214016766 2.528443452
2.306989 3.668361665 5.322198246
-5.555655 -12.81683497 30.86530248
-4.47221 24.84605585 20.00066228
-0.058048 0.259602846 0.00336957
2.640717 -0.15328834 6.973386274
2.169545 5.729154364 4.706925507
1.687697 3.661534588 2.848321164
-3.470548 -5.857233448 12.04470342
-4.500585 15.61949627 20.25526534
-4.227613 19.02673165 17.87271168
-3.920385 16.57387059 15.36941855
-0.088605 0.347365713 0.007850846
3.117916 -0.276262947 9.721400183
3.432668 10.70277048 11.7832096
3.33043 11.43226049 11.09176398
4.596884 15.30960038 21.13134251
2.143834 9.854956213 4.59602422
This is what you told me before, but I never got them the same value. Could you please confirm this information for me?

[startz]

Sounds like that should be close. I'm not sure whether it's exactly the same.

[cuongnh]

Sounds like that should be close. I'm not sure whether it's exactly the same.

Thanks Startz, you are still with me. In any books, I do not find exlanation or evidence for that inclusion of first value of residuals in e_t*e_t-1. They are not EXACTLY the same, but i think that is reasion of regression.
Dear Startz, I still want to have your answer to my question on transformation of data. E.g. I have original price data, let call it data1, after using first rho (rho1) to change data1 into new data, let call it data2, which will be used to regress again. From this regression, I can get second rho (rho2). Then, i want to repeat the procedure, means using second rho2 to change data again. At this stage, i dont know I have to use this rho2 with whether data1 or data2. Do you understand my question?

[startz]

Sounds like that should be close. I'm not sure whether it's exactly the same.

Thanks Startz, you are still with me. In any books, I do not find exlanation or evidence for that inclusion of first value of residuals in e_t*e_t-1. They are not EXACTLY the same, but i think that is reasion of regression.
Dear Startz, I still want to have your answer to my question on transformation of data. E.g. I have original price data, let call it data1, after using first rho (rho1) to change data1 into new data, let call it data2, which will be used to regress again. From this regression, I can get second rho (rho2). Then, i want to repeat the procedure, means using second rho2 to change data again. At this stage, i dont know I have to use this rho2 with whether data1 or data2. Do you understand my question?

data1

[cuongnh]

Sounds like that should be close. I'm not sure whether it's exactly the same.

Thanks Startz, you are still with me. In any books, I do not find exlanation or evidence for that inclusion of first value of residuals in e_t*e_t-1. They are not EXACTLY the same, but i think that is reasion of regression.
Dear Startz, I still want to have your answer to my question on transformation of data. E.g. I have original price data, let call it data1, after using first rho (rho1) to change data1 into new data, let call it data2, which will be used to regress again. From this regression, I can get second rho (rho2). Then, i want to repeat the procedure, means using second rho2 to change data again. At this stage, i dont know I have to use this rho2 with whether data1 or data2. Do you understand my question?

data1

So, you mean that the steps are done just for finding the best rho, and then apply it to the original data, dont you? Could you please give me some evidences to prove that idea? I am still unclear.

[cuongnh]

Dear Startz, I used C-O procedure, and the best estimation was right at the second time. I mean SSR, rho are smallest compared with that in other steps. I think that is the best estimation for my data. However, the Durbin Watson is still low, it is 1.17, and Adj. R Squared is just around .55. I am worried aout that. Do you have any ideas regarding this result?
I fact, I used one trend variable on the right side of the model. In details, I added a variable with value of 1 (1,1,1,1,1,1) for first half of the observations, the remainings take value from 1, 2, 3,4.... till the end. Then I squared those values, results from squaring were used as a dummy variable in my specification. I read from a certain book that, C-O procedure should not be applied to the model with trend variable. Could you please let me know if my model with that trend variable is right or wrong, should it be included in the model if I use C-O procedure?
Thank you very much for your helps!

[cuongnh]

Dear Startz, I am thinking that whether I should apply the Prais-Winsten for calculating the first observation or not. If not, it means that after each iteration of C-O procedure, one observation will be lost. I dont know what should be the way. Could please give me your ideas?

[startz]

Dear Startz, I am thinking that whether I should apply the Prais-Winsten for calculating the first observation or not. If not, it means that after each iteration of C-O procedure, one observation will be lost. I dont know what should be the way. Could please give me your ideas?

My advice is to use the built-in AR(1) procedure.