Solving Serial Correlation without Y(-1)

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Mihailo Savic
Posts: 12
Joined: Mon Jan 29, 2018 9:57 am

Solving Serial Correlation without Y(-1)

Postby Mihailo Savic » Sat Feb 24, 2018 2:25 pm

Hello,

I am running a simple Yt = c + bXt + Ut model.

My Durbin-Watson statistic is very low DW < dL, meaning that i have serial correlation.

One way to solve this is with the first difference model or a Cochrane - Orcutt model, where I would transform my model into:

Yt - rYt-1 = c(1-r) + b(Xt - rXt-1) + Ut - rUt-1 ->
-> Yt = a + b1Xt + b2Xt-1 + rYt-1 + Et.

This should eliminate the serial correlation problem.

However, the problem that I have is that (for my purposes) I cannot estimate Yt using Yt-1 (or any other lagged Y).

My question is: How can I get rid of serial correlation without involving Yt-1 in my model?

Regards.
Last edited by Mihailo Savic on Sun Feb 25, 2018 11:36 am, edited 1 time in total.

startz
Non-normality and collinearity are NOT problems!
Posts: 3775
Joined: Wed Sep 17, 2008 2:25 pm

Re: Solving Serial Correlation without Y(-1)

Postby startz » Sat Feb 24, 2018 3:04 pm

I assume this is a homework assignment. Take a look at AR(1) in the help system.

Mihailo Savic
Posts: 12
Joined: Mon Jan 29, 2018 9:57 am

Re: Solving Serial Correlation without Y(-1)

Postby Mihailo Savic » Sun Feb 25, 2018 10:38 am

This is not a homework assignment...

If any one could provide me with a method that solves serial correlation that doesn't involve a lagged dependent variable in the regression, that would be very helpful. It would also be helpful to tell me if anyone believes that such a method may not exit at all.

Mihailo Savic.

startz
Non-normality and collinearity are NOT problems!
Posts: 3775
Joined: Wed Sep 17, 2008 2:25 pm

Re: Solving Serial Correlation without Y(-1)

Postby startz » Sun Feb 25, 2018 11:55 am

It might help if you could explain why you can't use y(-1). Using AR(1) doesn't mention y(-1), but it's used implicitly. The same is true for using Newey-West standard errors. For that matter, y(-1) is used in computing the Durbin-Watson statistic.

Mihailo Savic
Posts: 12
Joined: Mon Jan 29, 2018 9:57 am

Re: Solving Serial Correlation without Y(-1)

Postby Mihailo Savic » Sun Feb 25, 2018 8:45 pm

Thanks for the response,

I am using a simple Yt = a + b*Xt +Ut model, where Yt are profits and Xt are revenues at time t and b is the coefficient beta.

I have a tested party "i". For "i" I can calculate the beta of "i".

I also have multiple comparable parties c1, c2, c3... For each of them I would find their betas.

The goal is to check if beta of "i" (the coefficient of the tested party) is similar to the beta of the comparables (it is supposed to be similar because the tested party and the comparables have similar characteristics).

If the tested party's beta "i" is much different from the beta (c1, c2, c3...) then the tested party may have done something unusual.

The problem is that the simple model that I am using has serial correlation.

However, I cannot use methods like Cochrane - Orcutt to fix serial correlation since the model I would end up with is Yt = a(1-r) + b*Xt - b*r*Xt-1 + r*Yt-1 + Et.

I cannot use this because if the tested party did something unusual this year then they probably did it last year as well, and therefore I shouldn't be allowed to use their previous year profits to estimate the current year profits.

So to repeat my question: How do I deal with the issue of serial correlation in my model without using methods with which I would end up with Yt-1 as one of the explanatory variables?

I hope I wasn't too confusing.

Mihailo.

startz
Non-normality and collinearity are NOT problems!
Posts: 3775
Joined: Wed Sep 17, 2008 2:25 pm

Re: Solving Serial Correlation without Y(-1)

Postby startz » Sun Feb 25, 2018 8:58 pm

You can use Newey-West (HAC) robust standard errors as an option in OLS. That will give you correct standard errors without changing the estimated coefficients. This does rely on a reasonable large sample. Also note that in testing coefficients across estimates there is an issue of correlation across equations. One way to handle this is to use system estimation.


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