How to do the second differencing in Stata?

[Minchul Park]

Consider the following long-form panel data example:

mata:
pid    = (1::100) # J(3, 1, 1)
period = J(100, 1, 1::3)
Y      = rnormal(300, 1, 0, 1)
X      = rnormal(300, 1, 0, 1)
end
getmata pid period Y X
xtset pid period

Here, I want to regress Y[t] - Y[t-2] on X[t] - X[t-2] (I think, the meaning of Y[t] is clear)
That is, I need to conduct the second difference.

At the first time, I tried to use the D. operator like below:

reg D2.(Y X)

But, you know, it is not what I want, because D2.Y is D.(D.Y) = Y[t] - 2Y[t-1] + Y[t-2].
So, is there any way to easily conduct the second (and higher order) difference in Stata?

[Maarten Buis]

gen d2y = y - l2.y
gen d2x = x - l2.x
reg d2y d2x

[Minchul Park]

Maarten Buis Thank you for your comment. Of course, we can manually generate the second differenced variables. But, in fact, what I want to do is to run a regression without generating new variables like below:

reg G.Y G.X

, where G. is the imaginary second differencing operator. Can we do this in Stata?

[Nick Cox]

Why not try it?

[Minchul Park]

Nick Cox In my real problem, I have to generate too many variables

gen d2Y = Y - l2.Y
gen d3Y = Y - l3.Y
...
gen d10Y = Y - l10.Y

gen d2X = X - l2.X
gen d3X = X - l3.X
...
gen d10X = X - l10.X

So, I want to just run the regression more compactly (specifically, I will run the regression with Mata's _stata command, so I want more compact one)

sureg (G2.Y G2.X) (G3.Y G3.X) ... (G10.Y G10.X)

where G. is the imaginary differencing operator.

Of course, Maarten Buis 's solution is perfect, but I am wondering whether there is a more compact way.

[Nick Cox]

You changed the question from regress to sureg, but no matter: The information you need is there in the help for sureg

depvar and the varlists may contain time-series operators; see tsvarlist.

But that doesn't extend to expressions involving two or more variables and/or two or more operators.

[Minchul Park]

Nick Cox Right, by simplifying the question I changed the question. I did not know the tsvarlist (may be time-series variable list). I will check the help file. Thank you so much.