Accepted Solutions
The responses given so far are quite good. I am not aware of any thing in SAS/ETS or (SAS/ECONOMETRICS) that is specifically designed for peak-discovery. I think this problem can also be called identifying turning points of a time series. For noisy time series the interest could be in finding the turning points of the underlying smooth signal. I will describe a quick way of doing this by using PROC UCM in SAS/ETS. Of course, this is a solution to a related problem and not the original one.
Let's say the value_t series can be thought of as a sum of mu_t, a smooth curve, and noise_t: value_t = mu_t + noise_t. The following code shows you how to fit this model when mu_t is modeled by an integrated random walk, which produces cubic smoothing spline, and Gaussian white noise:
proc ucm data=have;
id n interval=obs;
model value;
irregular;
level variance=0 noest;
slope plot=smooth;
forecast lead=0 outfor=for plot=decomp;
run;
The output data set "for" contains the estimates of mu_t and its slope (the columns s_level and s_slope). The turning points of mu_t could be located as places where the sign of adjacent s_level values change (i.e., points where s_level stops going upward/downward). These points are located by the following data steps:
data change;
set for(keep=n value s_level s_slope);
s1 = lag(s_slope);
turn = 0;
if n >= 2 then do;
if sign(s1) ^= sign(s_slope) then turn=1;
end;
run;
*The turns data set contains the discovered turn points: 5 17 24;
data turns;
set change;
where turn=1;
run;
The following plot shows how well s_level approximates the original series:
The following curve plots the slope (s_slope):
The following code shows the discovered turning points:
proc sgplot data=change;
title Plot of smoothed_value with identified turning points;
series x=n y=s_level;
refline 5 17 24/ axis=x;
run;
Of course, the identified turning points are not the turning points of the original series but of the underlying smooth signal. The following plot shows how they appear for the original curve:
proc sgplot data=change;
title Plot of value with identified turning points for smoothed_value;
series x=n y=value;
refline 5 17 24/ axis=x;
run;
I know this is a bit lengthy response.
calling @Rick_SAS
/*Here could give you a start*/
data have;
input value;
n+1;
datalines;
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proc iml;
use have;
read all var _num_ into Pts[c=vname];
close;
indices = cvexhull(Pts); /* compute convex hull of the N points */
hullIdx = indices[loc(indices>0)];
P = Pts[hullIdx, ];
call sort(p,2);
create p from p[c=vname];
append from p;
close;
quit;
data p2;
set p;
sign=sign(dif(value));
run;
data p3;
set p2;
by sign notsorted;
if last.sign;
run;
data want;
set have p3(rename=(n=_n value=_v));
run;
proc sgplot data=want;
series x=n y=value;
scatter x=_n y=_v/markerattrs=(symbol=starfilled color=red);
run;
The responses given so far are quite good. I am not aware of any thing in SAS/ETS or (SAS/ECONOMETRICS) that is specifically designed for peak-discovery. I think this problem can also be called identifying turning points of a time series. For noisy time series the interest could be in finding the turning points of the underlying smooth signal. I will describe a quick way of doing this by using PROC UCM in SAS/ETS. Of course, this is a solution to a related problem and not the original one.
Let's say the value_t series can be thought of as a sum of mu_t, a smooth curve, and noise_t: value_t = mu_t + noise_t. The following code shows you how to fit this model when mu_t is modeled by an integrated random walk, which produces cubic smoothing spline, and Gaussian white noise:
proc ucm data=have;
id n interval=obs;
model value;
irregular;
level variance=0 noest;
slope plot=smooth;
forecast lead=0 outfor=for plot=decomp;
run;
The output data set "for" contains the estimates of mu_t and its slope (the columns s_level and s_slope). The turning points of mu_t could be located as places where the sign of adjacent s_level values change (i.e., points where s_level stops going upward/downward). These points are located by the following data steps:
data change;
set for(keep=n value s_level s_slope);
s1 = lag(s_slope);
turn = 0;
if n >= 2 then do;
if sign(s1) ^= sign(s_slope) then turn=1;
end;
run;
*The turns data set contains the discovered turn points: 5 17 24;
data turns;
set change;
where turn=1;
run;
The following plot shows how well s_level approximates the original series:
The following curve plots the slope (s_slope):
The following code shows the discovered turning points:
proc sgplot data=change;
title Plot of smoothed_value with identified turning points;
series x=n y=s_level;
refline 5 17 24/ axis=x;
run;
Of course, the identified turning points are not the turning points of the original series but of the underlying smooth signal. The following plot shows how they appear for the original curve:
proc sgplot data=change;
title Plot of value with identified turning points for smoothed_value;
series x=n y=value;
refline 5 17 24/ axis=x;
run;
I know this is a bit lengthy response.
I tested rselukar 's code and got this :
data have;
set sashelp.stocks;
if stock='Intel';
keep date stock close;
run;
proc sort data=have;by date;run;
data have2;
set have(keep=close rename=(close=value));
n+1;
run;
proc ucm data=have2;
id n interval=obs;
model value;
irregular;
level variance=0 noest;
slope plot=smooth;
forecast lead=0 outfor=for plot=decomp;
run;
data change;
set for(keep=n value s_level s_slope);
s1 = lag(s_slope);
turn = 0;
if n >= 2 then do;
if sign(s1) ^= sign(s_slope) then turn=1;
end;
run;
data turns;
set change;
where turn=1;
run;
data all;
set have2 turns(keep=n value rename=(n=_n value=_v));
run;
proc sgplot data=all;
title Plot of smoothed_value with identified turning points;
series x=n y=value;
scatter x=_n y=_v/markerattrs=(symbol=starfilled color=red);
run;
