For reference because I always end up having to look this up:
lag: L, L2, … : gen lag2Var = L2.var
lead: F, F2, … : gen lead2Var = F2.var
difference: D, D2, … : gen diffofdiffVar = D2.var
seasonal difference: S, S2, … : gen seadiffVar = S2.var
I have never used the seasonal difference. I assume it depends on the seasonal frequency defined via tsset.
D2 is defined as [y(t)-y(t-1)] - [y(t-1)-y(t-2)], and not y(t)-y(t-2). For y(t)-y(t-2), if there are no gap in the time variable, you can use y(_n)-y(_n-2).
Reference: Forecasting in STATA: Tools and Tricks [Economic Forecasting (Econ 390) Spring 2010]
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