Standard error calculation using log transformation

[Stephanievermeer]

Hi Everyone!!

I have a question about the standard errors which Eviews calculates when you make a forecast. A simple example:

When I have the regression
log(X) c

I can make a forecast of the variable X and of the variable log(X), and I can save the mean and standard error of them! I'm currently working with an more complex regression, but I want to transform the mean and standard error from the forecast from the variable log(X) to X. So I have mean_logx and se_logx. To get the mean for the variable x I make the calculation:

mean_x = @exp(mean_logx) This works, I get the identical mean_x which Eviews gives me.

But then the se... I assume log(X) is normal distributed, so X is lognormal distributed. So the standard deviation is then:

stdev_x = @sqrt(@exp(stdev_logx^2)-1)*@exp(mean_logx) When I use for stdev_logx the se_logx... I don't get the same results as Eviews gives me...

What's is the problem.. I really need an answer :) How does Eviews calculates the standard error when he makes a forecast..?

Thanks in advance!!

[Stephanievermeer]

Is there anyone who knows the answer on my question? Do you understand my question?

[EViews Gareth]

EViews uses the delta method to calculate the standard errors. Roughly speaking the delta method says:

Code: Select all

VAR(f(X)) = f'(X)^2*VAR(X)

(i.e. the square of the derivative of the function multiplied by the variance of the variable). Note if you're doing standard errors, you remove the square

Thus in your case the standard errors are roughly:

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SE(Log(y_forecast)) = d(Log(y_forecast))/dy * SE(Y_forecast) = (1/Y_forecast)*SE(Y_forecast)

[dagfinnrime]

Hi,

To figure out SE-bands with lagged dependent, and log-transformation, one use the same methodology?

Thanks in advance,
Dagfinn