Working with dates

#how to set and format dates

gen new_date_variable=date(date_variable ,"YMD")
format date_new %td

or 

gen new_date_variable=date(date_variable ,"DMY")
format date_new %tw

%tc Daytime   01jan1960 00:00:00
%td Daily     01jan1960
%tw Weekly    1960w1
%tm Monthly   1960m1
%tq Quarterly 1960q1
%ty yearly    0  
## how to use if conditions with dates

>gen season=.
>replace season=1 if Injury_Date >= date("01012015","DMY") & Injury_Date<= date("21032015","DMY") | Injury_Date >= date("21122015","DMY") & Injury_Date<= date("21032016","DMY") | Injury_Date >= date("21122016","DMY") & Injury_Date<= date("21032017","DMY") | Injury_Date >= date("21122017","DMY")
>replace season=2 if Injury_Date >= date("21032015","DMY") & Injury_Date<= date("21062015","DMY") | Injury_Date >= date("21032016","DMY") & Injury_Date<= date("21062016","DMY") | Injury_Date >= date("21032017","DMY") & Injury_Date<= date("21062017","DMY")
>replace season=3 if Injury_Date >= date("21062015","DMY") & Injury_Date<= date("21092015","DMY") | Injury_Date >= date("21062016","DMY") & Injury_Date<= date("21092016","DMY") | Injury_Date >= date("21062017","DMY") & Injury_Date<= date("21092017","DMY") 
>replace season=4 if Injury_Date >= date("21092015","DMY") & Injury_Date<= date("21122015","DMY") | Injury_Date >= date("21092016","DMY") & Injury_Date<= date("21122016","DMY") | Injury_Date >= date("21092017","DMY") & Injury_Date<= date("21122017","DMY") 

label define season 1 winter 2 spring 3 summer 4 fall

label values season season

How to model using dates.
Assuming we want to fit a fourth order auto-regressive model:

Y_t=μ+β_1yt-1+ β_2yt-2 + β_3yt-3 + β_4yt-4 + ε

There are two ways to go about using lag variables:

gen y1 = y[_n-1]

gen y2 = y[_n-2]

gen y3 = y[_n-3]

gen y4 = y[_n-4]

regress y y1 y2 y3 y4

After setting the data into ts mode we can use the L operator to indicate lag variables

regress y L.y L2.y L3.y L4.y

or

regress L(0/4).y

The lead operator F is the inverse of L. Where F.y indicates yt+1.

The lead operator D indicates the arithmetical difference of adjacent observations Where D.y indicates  Δ≡y_t-y_t-1 

and

D2.y indicates  Δ≡y_t-y_t-2