Plotting a curve with trigonometric functions

[Amos Machado]

I need to plot a curve as y = f(t), where t is the time, in the following way.
y= 0 at t=-5
- first interval t=-5 to t=0: y slightly increasing
-second interval t=0 to t=5: y slightly increasing
-third interval t=5 to t= 10: y increasing at an increasing rate
-forth interval t=10 to t=15: y increasing at a decreasing rate
-fifth interval (smaller) t=15 to t=18: y unchanged
-sixth interval(smaller) t=18 to t=21: y decreasing at an increasing rate
-seventh interval (smaller) t=21 to t=24: y decreasing at a decreasing rate

I am unable to get the exact required shape.
Please note that the t values for intervals are just to explain the shape so they can be different. I think this can better be done by using trigonometric function. Any help in this regard!

[William Lisowski]

I doubt that a trigonometric function will help since - as best as I recall 50+ years out - you're not going to get a flat portion to deal with the 15-to-18 range.

The output of help graph twoway lists a number of graph types, one of which may help you.

    mspline               spline line plot
    lowess                LOWESS line plot
    lfit                  linear prediction plot
    qfit                  quadratic prediction plot
    fpfit                 fractional polynomial plot

If you were to provide y values corresponding to the x values you give, someone on Statalist might be interested in providing example code. As your question now stands, many readers will be reluctant to spend much time on a problem so poorly specified.

[Amos Machado]

ThanksWilliam.
I tried but maybe the question was clear enough. Here is the type of curve I need but I seek a better way to perform this task.

clear
input t y
-5 0
-4 1
-3 2
-2 3
-1 4
0 5
1 7
2 9
3 11
4 13
5 15
6 18
7 22
8 27
9 33
10 40
11 44
12 47
13 49
14 50
15 50
16 50
17 50
18 49
19 47
20 44
21 40
22 35
23 33
24 31
25 30

end
tsset t
tssmooth ma y_ = y , window(2 1 2)
line y_ t, ylabel("") yti("") xti("") xlabel("") ///
    graphregion(fcolor(white) lcolor(white)) aspect(0.3)

[William Lisowski]

I think you can improve on what you have by adjusting things a little more.

Below is the code I used to play with the data, ultimately creating the plot points given by z. By overlaying the plot points on the line, I could better see the relationship of the line to the points. By including vertical lines at each of the x values where the curve changes, to help judge how the line is meeting expectations. I found that window(1,1,1) gave better results. Given that you said you wanted the curve unchanged between 15 and 18 I was surprised to see your data unchanging between 14 and 17.

clear all
clear
* Example generated by -dataex-. To install: ssc install dataex
clear
input float(t y z)
-5  0  0
-4  1  1
-3  2  2
-2  3  3
-1  4  4
 0  5  5
 1  7  7
 2  9  9
 3 11 11
 4 13 13
 5 15 15
 6 18 18
 7 22 22
 8 27 27
 9 33 33
10 40 40
11 44 46
12 47 51
13 49 55
14 50 58
15 50 60
16 50 60
17 50 60
18 49 60
19 47 59
20 44 56
21 40 50
22 35 44
23 33 40
24 31 37
25 30 36
end

cls
tsset t
tssmooth ma y_ = y , window(1 1 1)
line y_ t || scatter y t, xline(0 5 10 15 18 21 24) name(tss1) 

tssmooth ma z_ = z , window(1 1 1)
line z_ t || scatter z t, xline(0 5 10 15 18 21 24) name(tss2) 

line y_ z_ t, xline(0 5 10 15 18 21 24) ///
    ylabel("") yti("") xti("") xlabel("") ///
    graphregion(fcolor(white) lcolor(white)) aspect(0.3)