How to correct a Dummy variable for Autocorrelation?

[Martin B]

Hi at all!

This question actually follows from another thread. However, I thought it would be useful to post it separately.

I have the following regression equation system:

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y_1t = a + b_1*x_t + c*z_1t y_2t = a + b_2*x_t + c*z_2t

Now, if I want to correct for autocorrelation, I can write (e.g. for the first equation)

Code: Select all

y_1t = a*(1-r) + b_1*(x_t-r*x_{t-1}) + c*(z_1t-r*z_1{t-1}) + r*y_1{t-1}

Now, a dummy variable is included in the regression system of the sort

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y_1t = a + b_1*x_t + c*z_1t + g*D*z_1t y_2t = a + b_2*x_t + c*z_2t + g*D*z_2t

Here, D can take either 1 or 0 and g is the coefficient before the Dummy variable.
My question is: how can I correct the Dummy variable for possible autocorrelation? Is it even important? The problem is: it is a dummy indicating 1 if the observation is after a certain date and 0 if the observation is before a certain date. So, after some time, all observations will have D=1.

I thank you very much.

Kind regards

M

[startz]

Hi at all!

This question actually follows from another thread. However, I thought it would be useful to post it separately.

I have the following regression equation system:

Code: Select all

y_1t = a + b_1*x_t + c*z_1t y_2t = a + b_2*x_t + c*z_2t

Now, if I want to correct for autocorrelation, I can write (e.g. for the first equation)

Code: Select all

y_1t = a*(1-r) + b_1*(x_t-r*x_{t-1}) + c*(z_1t-r*z_1{t-1}) + r*y_1{t-1}

Now, a dummy variable is included in the regression system of the sort

Code: Select all

y_1t = a + b_1*x_t + c*z_1t + g*D*z_1t y_2t = a + b_2*x_t + c*z_2t + g*D*z_2t

Here, D can take either 1 or 0 and g is the coefficient before the Dummy variable.
My question is: how can I correct the Dummy variable for possible autocorrelation? Is it even important? The problem is: it is a dummy indicating 1 if the observation is after a certain date and 0 if the observation is before a certain date. So, after some time, all observations will have D=1.

I thank you very much.

Kind regards

M

You treat the dummy variable exactly like any other rhs variable.

[Martin B]

Hi Startz

Thank you for your answer.

So I can do the following?

Code: Select all

y_1t = a*(1-r) + b_1*(x_t-r*x_{t-1}) + c*(z_1t-r*z_1{t-1}) + r*y_1{t-1} + g*D*(z_1t-r*z_1{t-1})

[startz]

Hi Startz

Thank you for your answer.

So I can do the following?

Code: Select all

y_1t = a*(1-r) + b_1*(x_t-r*x_{t-1}) + c*(z_1t-r*z_1{t-1}) + r*y_1{t-1} + g*D*(z_1t-r*z_1{t-1})

Not quite. My answer was a little careless. You need to treat D*z_1 as the RHS variable.

Code: Select all

y_1t = a*(1-r) + b_1*(x_t-r*x_{t-1}) + c*(z_1t-r*z_1{t-1}) + r*y_1{t-1} + g*(D*z_1t-r*D{t-1}*z_1{t-1})

[Martin B]

Thank you very much!

I already tested in Eviews. Coefficient before the dummy proved to be statistically insignificant. But at least I know now...

Kind regards

M