How do i get cumulative decayed sum?

[Jhpark1222]

Hi I am currently struggling to get a cumulative 'decayed' sum of variables.

For example, if variable y has value like:

day  y

1      4

2      3

3      2

4      6

5      1

6      2

i want to get a variable 'desumy', by each person (let's assume that example that i brought is from a single person),  assuming that decaying rate is 0.5 in a day:

day  y   desumy

1      4       0

2      3      4*0.5

3      2      4*0.5*0.5 + 3*0.5

4      6      4*0.5*0.5*0.5 + 3*0.5*0.5

5      1      4*0.5*0.5*0.5 + 3*0.5*0.5

6      2

i figured out that all i have to do is to create variable 'desumy' that satisfies

desumy_t = (desumy_t-1 + y_t-1)*0.5, but i am struggling to make a code implementing what i want.

Thank you.

[Ksharp]

You want this ?

data have;
input day  y;
cards;
1      4
2      3
3      2
4      6
5      1
6      2
;

data want;
 set have;
 retain  lag_desumy 0;
 desumy=sum(lag_desumy,lag(y))*0.5;
 lag_desumy=desumy;
 drop lag_desumy;
run;

[Jhpark1222]

Thanks a lot for your reply.

I am trying to use this in proc nlmixed in order to estimate maximum likelihood, but in proc nlmixed, 'retain ' seems to not work.

0.5 in my original question was decay rate phro, which is a parameter that needs to be estimated through maximum likelihood estimation process.

is there any advice?

[Tom]

Just use retain and lag().  It is even easier if you use a sum statement as then the target variable of the sum statement is automatically retained.

data want;
  set have;
  desumy + lag(y)*0.5 ;
run;

[Jhpark1222]

Thanks a lot for your reply.

I am trying to use this in proc nlmixed in order to estimate maximum likelihood, but in proc nlmixed, 'retain ' seems to not work.

0.5 in my original question was decay rate phro, which is a parameter that needs to be estimated through maximum likelihood estimation process.

is there any advice?

[Ksharp]

Calling @StatDave  @SteveDenham  @lvm 

[SteveDenham]

Not real sure this approach will work, but you might try arranging your data  so that each desumy and y are read in as input, and desumy_t is a dependent variable.  Then you could fit this

desumy_t = (desumy_t-1 + y_t-1)*prho;

assuming some sort of count related distribution (poisson, negbin or generalized poisson).

SteveDenham