how to get levels from forecasted differenced data

[Fregensburg]

Hi all,

I have non-stationary series, say bond data, that are logged and differenced.
(raw data: ust10y, from which dlnust10y=lnust10y-lnust10y(-4)).
From that, I get a series of forecasted values (dlnust10yf).
Since what I want is actual yields, I need to back out the unlogged levels.To do this, I need first to un-difference, then take exponentials. The second step is obvious (i.e. series ust10yf = exp(lnust10yf) . What about the first?
So I want lnust10yf = dlnust10yf + lnust10yf(-4) but all I have is dlnust10yf, because I forecasted the dlnust10y rather than lnust10y (Duh! –just trying to be pendantically clear).
Any thoughts? Is it possible? If so how?

[EViews Gareth]

Easiest just to estimate the equation with dlog(ust10y,4) as the dependent variable, and let EViews handle the forecasting for you.

[Fregensburg]

Easiest just to estimate the equation with dlog(ust10y,4) as the dependent variable, and let EViews handle the forecasting for you.

Could you be more precise? I'm not sure I follow you. Maybe I'm being a little dense, but is there references in the manuals for this? And, what you mention is something that can be done with all type of models?

[EViews Gareth]

You have a series called ust10y. From that, I assume, you created a new series called dlnust10y which is equal to the 4-period difference of the logs of ust10y. You then estimated an equation using dlnust10y as the dependent variable.

I'm saying don't do that. Simply estimate the equation with dlog(ust10y,4) as the dependent variable. When you forecast from that equation EViews will recognise that you have a function as the dependent variable and will ask whether you want to forecast the function or the underlying variable. In your case you want to forecast the underlying variable. EViews will do the de-log and the de-difference for you.

[Fregensburg]

You have a series called ust10y. From that, I assume, you created a new series called dlnust10y which is equal to the 4-period difference of the logs of ust10y. You then estimated an equation using dlnust10y as the dependent variable.

I'm saying don't do that. Simply estimate the equation with dlog(ust10y,4) as the dependent variable. When you forecast from that equation EViews will recognise that you have a function as the dependent variable and will ask whether you want to forecast the function or the underlying variable. In your case you want to forecast the underlying variable. EViews will do the de-log and the de-difference for you.

Ok, got you. so I'm assuming a dialogue window will crop up- if I'm running a program what lines do I need to tell eviews what to do?

[EViews Gareth]

Nothing really. By default EViews will forecast the underlying series

[Fregensburg]

Nothing really. By default EViews will forecast the underlying series

thanks. I noticed however that the VAR R^2 (not that I care much about that, trusting R^2 is a bit getting news from the Sun) shoots up from 0.65 (prior value) to 0.8 now that I express the tranformed series as functions. Can't check the rest of it because I've gone home now, but I suspect this type of discrepancy carries through in the rest of the analysis. That worries me. I imagine a statistic like that shouldn't change, and it's just something I overlooked, right?

thanks ever so much.

[EViews Gareth]

Should give identical results in every way. For example:

Code: Select all

create m 1990 2020 rndseed 1 series ust10y = rnd series exog = nrnd series lust = log(ust10y) series dlust = d(lust,4) equation eq1.ls dlog(ust10y,4) c exog equation eq2.ls dlust c exog show eq1 show eq2

[Fregensburg]

I'm unsure why, but in my program, when I compare estimations, it turns out that only way to get the equivalent of using series such as:

dlnust10y = lnust10y-lnust10y(-4))

is to use expressions that involve taking seasonal differences, i.e:

dlnust10y = dlog(ust10y,0,4)

rather than resorting to dlog(ust10y,4).

When I do use the expression for seasonal differences, the estimations I get are equivalent to what I got from using the 1st specification (i.e: dlnust10y = lnust10y-lnust10y(-4)), and that doesn't square with what you posted and with what the manual says (UserGuide I, p. 170-171).

The estimates, however, are not equivalent when I estimate a state space model -the model simply fails to converge. Previously, that estimation seemed to be working completely fine. So my question is: why would that be the case?