Delta Method_Standard Errors_Dissertation

[roronoaroronoa]

Hi All,

I am trying to complete my dissertation and I am asking your help. The situation is the following:

Let's say that we have two series δ and δ'. We run a regression of δ' against δ and some other variables and the result is :δ'=1.032δ-0.078k-0.776z where the standard errors are 0.076, 0.046 and 0.101 respectively. I would like to test the restrictions σ(δ)/σ(δ΄)=1 and correl(δ,δ')=1 but I do not know how to calculate the standard errors. My supervisor suggested me to use the Delta Method but all the examples I have found use the delta method to test restrictions which are functions only of the variables of the RHS of the regression model, i.e. b1,b2 etc. Do you know how can I calculate the standard errors for the above restrictions? Unfortunately , I do not have a maths-related bachelor (accounting) and thus I decided to post here. It is not a matter of laziness. Thanks in advance for any help and I hope there is someone out there that enjoys the summer because I do not! :( Again, any ideas are appreciated!

[startz]

In a regression, one usually wants to test restrictions about the parameters of the equation. Is that what you're trying to do?

[roronoaroronoa]

Thanks for the immediate response! Let me explain myself better. I have an actual series δ (log dividend-price ratio) and I run a 3 lag VAR between δ and Dd (Dividend growth). I use the VAR (written in companion form) to generate a forecasted series of the δ which I call it δ'. What I want is to test if σ(δ)/σ(δ')=1 and if correl(δ,δ')=1. I can calculate the σ(δ)/σ(δ') and correl(δ,δ') using the actual δ and the forecasted δ'. But i do not know how to caclulate the standard errors of these restrictions. Let us assume that the δ series follows a normal distribution. How can i procceed to the caclulation of the standard errors of the above restrictions?

ps: After the above, I run a regression of δ' against δ and some other variables and the result is :δ'=1.032δ-0.078k-0.776z. Does this help?

Kind regards

[startz]

I'm not sure that this is going to be very helpful, but...

What you're trying to do doesn't make sense. The usual hypothesis test concerns the value of an unobserved parameter. Here you observe both series you're interested in. If you want to know what the correlation is, just calculate it. Either it's one or it isn't.

[roronoaroronoa]

Thanks startz for your reply and your time. I will try to find a solution.

Kind Regards