Forecast errors for geometric random walk

[Per]

Hi!

I am trying to generate confidence intervals for a k step prediction of a geometric random walk with drift.

First, I estimate the drift parameter by running a least squares regression on DLOG(X) on data from 1950-2011 as per below, whereby the constant (C) in the regression is the point estimate for the drift parameter. I then make forecasts of X (i.e. original series, not dlog) for 2012 to 2070 using EViews built in forecast feature, and also enable the option to output forecast errors. This gives me a series of forecast errors as a new variable.

1. What's the interpretation of these forecast errors? Specifically, are they the forecast error of k step ahead forecasts of the level of the original series X, for each year 2012-2070?
2. How are the forecast errors calculated?
3. What I would really like to do in the end is to achieve a x% prediction confidence interval for the level of X. Is there any way to achieve this using EViews' built in features, or do I have to calculate those myself using the standard errors of the regression?

Many thanks!
Per


Dependent Variable: DLOG(X)
Method: Least Squares
Date: 05/03/16 Time: 09:14
Sample (adjusted): 1951 2011
Included observations: 61 after adjustments

Variable Coefficient Std. Error t-Statistic Prob.

C 0.007820 0.003431 2.279500 0.0262

R-squared 0.000000 Mean dependent var 0.007820
Adjusted R-squared 0.000000 S.D. dependent var 0.026793
S.E. of regression 0.026793 Akaike info criterion -4.385079
Sum squared resid 0.043073 Schwarz criterion -4.350474
Log likelihood 134.7449 Hannan-Quinn criter. -4.371517
Durbin-Watson stat 1.445670

[Per]

Hi again,

To partly answer my own questions (if anyone else is interested), and reiterate the questions I still don't understand.

1. According to chapter 23 of the Eviews manual, forecast errors for a non-linear transformation will be a) exact in the +-2 sterror output graph generated by the forecast function but only b) linear approximations for the forecast error series. Isn't this a bit strange - if EViews is capabable of calculating/transforming the exact standard errors for outputting the confidence interval in the graph, it should be able to also output the same standard errors to a series for subsequent use? Perhaps I'm missing something?

2. This question remains. I would be very grateful if someone could explain/direct my to a source where I can see how EViews calculates forecast standard errors (both with and without parameter errors, and especially for models that use lagged terms such as mine).

3. It seems I have to do this manually according to my findings in 1. I.e. for my case, one would have to estimate D(LOG X) instead of DLOG(X), use the standard errors of that regression, calculate a confidence interval, and then transform to the level variable through EXP(LOG X +- 1.96*SE(LOGX)) to get a 95% CI.