topic Re: Estimate transition probability matrix in SAS Programming

Estimate transition probability matrix

Ruslan — Mon, 05 Oct 2015 19:50:04 GMT

Dear All,

Could you please help me to estimate the following probability transition matrix?

I have companies each month with certain values like this:

Month Company Value

1 1 10

1 2 14

1 5 15.5

1 7 8

1 9 3

1 10 11

1 13 16

1 15 12

1 16 19

1 18 7

1 20 11

1 21 5

1 22 8

2 1 9

2 2 13

2 3 20

2 4 2

2 5 19

2 8 9

2 10 10

2 11 7

2 12 13

2 13 3

2 15 20

2 16 23

2 18 17

2 20 21

2 21 8

I need to do the following. First, sort companies in ascending order into ten groups (portfolios) each month (in total I have 203 months) based on their value. Second, I need to obtain the average of the month-to-month transition matrices for the companies in these groups i.e. the average probability (in percent) that a company in group i (presumably, given by the rows of the matrix) in one month will be in group j (possibly given by the columns of the matrix) in the subsequent month.

So the martrix should be something like this:

1 2 3 4 5 6 7 8 9 10

1 prob(firm in group 1 in month t remains to be in group 1 in month t+1)

2 prob(firm in group 2 in month t moves to group 1 in month t+1)

3 ...

4 ...

5 ...

6 ...

7 ...

8 ...

9 ...

10 prob(firm in group 10 in month t moves to group 1 in month t+1)

I would hugely appreciate any help since I have spent entire day attempting to write a code, but got nothing at the end of the day. Please, please help me with this matrix.

Kind regards,

Ruslan

Re: Estimate transition probability matrix

Rick_SAS — Mon, 05 Oct 2015 20:44:29 GMT

What tools are you using? Do you have SAS/ETS software (PROC ENTROPY) or SAS/IML software? Or are you trying to compute this in Base SAS?

Re: Estimate transition probability matrix

Ruslan — Mon, 05 Oct 2015 20:56:56 GMT

Hi Rick.

It does not really matter. I have both ETS and IML, so any suggestions on how to construct this matrix in any of those softwares will be hugely appreciated.

Kind regards,

Ruslan

Re: Estimate transition probability matrix

PGStats — Mon, 05 Oct 2015 20:58:03 GMT

I had to simulate data to get a meaningful example...

data have;
call streaminit(85765);
do month = 1 to 10;
    do Company =   1, 2, 5, 7, 9, 10, 13, 15, 16, 18, 20, 21, 22;
        value = round(rand("UNIFORM") * 25, 0.5);
        output;
        end;
    end;
run;

proc rank data=have out=haveRanks groups=10;
by month;
var value;
ranks group;
run;

proc sql;
create table trans as
select a.group as from, b.group as to, count(*) as nTrans
from haveRanks as a inner join haveRanks as b
    on a.company=b.company and a.month+1 = b.month
group by a.group, b.group;
create table probs as 
select from, to, nTrans/sum(nTrans) as prob
from trans
group by from;
quit;

proc transpose data=probs out=transTable(drop = _name_) prefix=to_;
by from;
id to;
var prob;
run;

/* reorder variables, assign format to probabilities (optional) */
data transTable;
retain from to_0-to_9;
format to_0-to_9 pvalue5.3;
set transTable;
run;

proc print data=transTable noobs; run;