## Joint probability distribution of three variable

Solved
Occasional Contributor
Posts: 7

# Joint probability distribution of three variable

I have used this for program for copula simulation

data returns;
input ret_x ret_y ret_z;
cards;
0.004182 0.003503 0.584
-0.027960 -0.000582 0.54
0.006732 0.025611 0.14
-0.033435 -0.002838 -0.24
0.029560 0.010814 -0.4
-0.003054 -0.001689 0.8
-0.012255 -0.012408 0.9
0.013958 0.003427 0.14
-0.011318 -0.017075 0.14
-0.022587 0.002316 0.28
;
/* Copula estimation */
proc copula data = returns;
var ret_x ret_y ret_z;
fit normal / outcopula=estimates;
/* keep only correlation estimates */
data estimates;
set estimates;
keep ret_x ret_y ret_z;
/* Copula simulation */
proc copula;
var ret_x ret_y ret_z;
define cop normal (cor = estimates);
simulate cop / ndraws = 500
outuniform = simulated_uniforms
plots=(data=uniform scatter);
run;

Got this log :

1 OPTIONS NONOTES NOSTIMER NOSOURCE NOSYNTAXCHECK;
70
71 data returns;
72 input ret_x ret_y ret_z;
73 cards;

NOTE: The data set WORK.RETURNS has 10 observations and 3 variables.
NOTE: DATA statement used (Total process time):
real time 0.00 seconds
user cpu time 0.00 seconds
system cpu time 0.00 seconds
memory 521.87k
OS Memory 28840.00k
Timestamp 03/30/2018 10:48:35 AM
Step Count 50 Switch Count 2
Page Faults 0
Page Reclaims 131
Page Swaps 0
Voluntary Context Switches 10
Involuntary Context Switches 0
Block Input Operations 0
Block Output Operations 272

84 ;

85 /* Copula estimation */
86 proc copula data = returns;
87 var ret_x ret_y ret_z;
88 fit normal / outcopula=estimates;
89 /* keep only correlation estimates */

NOTE: The data set WORK.ESTIMATES has 3 observations and 9 variables.
NOTE: PROCEDURE COPULA used (Total process time):
real time 0.04 seconds
user cpu time 0.04 seconds
system cpu time 0.00 seconds
memory 2572.53k
OS Memory 30124.00k
Timestamp 03/30/2018 10:48:35 AM
Step Count 51 Switch Count 2
Page Faults 0
Page Reclaims 517
Page Swaps 0
Voluntary Context Switches 9
Involuntary Context Switches 0
Block Input Operations 0
Block Output Operations 272

90 data estimates;

91 set estimates;
92 keep ret_x ret_y ret_z;
93 /* Copula simulation */

NOTE: There were 3 observations read from the data set WORK.ESTIMATES.
NOTE: The data set WORK.ESTIMATES has 3 observations and 3 variables.
NOTE: DATA statement used (Total process time):
real time 0.00 seconds
user cpu time 0.00 seconds
system cpu time 0.00 seconds
memory 801.06k
OS Memory 30124.00k
Timestamp 03/30/2018 10:48:35 AM
Step Count 52 Switch Count 2
Page Faults 0
Page Reclaims 143
Page Swaps 0
Voluntary Context Switches 9
Involuntary Context Switches 0
Block Input Operations 0
Block Output Operations 264

94 proc copula;

95 var ret_x ret_y ret_z;
96 define cop normal (cor = estimates);
___
1
WARNING 1-322: Assuming the symbol CORR was misspelled as cor.
97 simulate cop / ndraws = 500
98 outuniform = simulated_uniforms
99 plots=(data=uniform scatter);
____
22
202
ERROR 22-322: Syntax error, expecting one of the following: ), DATATYPE, DISTRIBUTION, NONE.
ERROR 202-322: The option or parameter is not recognized and will be ignored.
100 run;

NOTE: The SAS System stopped processing this step because of errors.
WARNING: The data set WORK.SIMULATED_UNIFORMS may be incomplete. When this step was stopped there were 0 observations and 0
variables.
WARNING: Data set WORK.SIMULATED_UNIFORMS was not replaced because this step was stopped.
NOTE: PROCEDURE COPULA used (Total process time):
real time 0.00 seconds
user cpu time 0.00 seconds
system cpu time 0.00 seconds
memory 339.25k
OS Memory 29864.00k
Timestamp 03/30/2018 10:48:35 AM
Step Count 53 Switch Count 0
Page Faults 0
Page Reclaims 52
Page Swaps 0
Voluntary Context Switches 0
Involuntary Context Switches 0
Block Input Operations 0
Block Output Operations 16

101
102
103 OPTIONS NONOTES NOSTIMER NOSOURCE NOSYNTAXCHECK;
115

Accepted Solutions
Solution
‎03-31-2018 04:06 AM
SAS Super FREQ
Posts: 4,245

## Re: Joint probability distribution of three variable

You didn't mention what version of SAS you are running, but here is a link to the most recent doc.

1. The correct syntax for the DEFINE statement is

define cop normal (corr = estimates);

2. The correct syntax for the PLOTS option is

plots=(datatype=uniform);

If you are using an older version of SAS that might have different syntax, consult the documentation for your version.

All Replies
Occasional Contributor
Posts: 7

## Joint probability distribution estimation of three variables using copulas

I have used this for program for copula simulation

data returns;
input ret_x ret_y ret_z;
cards;
0.004182 0.003503 0.584
-0.027960 -0.000582 0.54
0.006732 0.025611 0.14
-0.033435 -0.002838 -0.24
0.029560 0.010814 -0.4
-0.003054 -0.001689 0.8
-0.012255 -0.012408 0.9
0.013958 0.003427 0.14
-0.011318 -0.017075 0.14
-0.022587 0.002316 0.28
;
/* Copula estimation */
proc copula data = returns;
var ret_x ret_y ret_z;
fit normal / outcopula=estimates;
/* keep only correlation estimates */
data estimates;
set estimates;
keep ret_x ret_y ret_z;
/* Copula simulation */
proc copula;
var ret_x ret_y ret_z;
define cop normal (cor = estimates);
simulate cop / ndraws = 500
outuniform = simulated_uniforms
plots=(data=uniform scatter);
run;

Got this log :

1 OPTIONS NONOTES NOSTIMER NOSOURCE NOSYNTAXCHECK;
70
71 data returns;
72 input ret_x ret_y ret_z;
73 cards;

NOTE: The data set WORK.RETURNS has 10 observations and 3 variables.
NOTE: DATA statement used (Total process time):
real time 0.00 seconds
user cpu time 0.00 seconds
system cpu time 0.00 seconds
memory 521.87k
OS Memory 28840.00k
Timestamp 03/30/2018 10:48:35 AM
Step Count 50 Switch Count 2
Page Faults 0
Page Reclaims 131
Page Swaps 0
Voluntary Context Switches 10
Involuntary Context Switches 0
Block Input Operations 0
Block Output Operations 272

84 ;

85 /* Copula estimation */
86 proc copula data = returns;
87 var ret_x ret_y ret_z;
88 fit normal / outcopula=estimates;
89 /* keep only correlation estimates */

NOTE: The data set WORK.ESTIMATES has 3 observations and 9 variables.
NOTE: PROCEDURE COPULA used (Total process time):
real time 0.04 seconds
user cpu time 0.04 seconds
system cpu time 0.00 seconds
memory 2572.53k
OS Memory 30124.00k
Timestamp 03/30/2018 10:48:35 AM
Step Count 51 Switch Count 2
Page Faults 0
Page Reclaims 517
Page Swaps 0
Voluntary Context Switches 9
Involuntary Context Switches 0
Block Input Operations 0
Block Output Operations 272

90 data estimates;

91 set estimates;
92 keep ret_x ret_y ret_z;
93 /* Copula simulation */

NOTE: There were 3 observations read from the data set WORK.ESTIMATES.
NOTE: The data set WORK.ESTIMATES has 3 observations and 3 variables.
NOTE: DATA statement used (Total process time):
real time 0.00 seconds
user cpu time 0.00 seconds
system cpu time 0.00 seconds
memory 801.06k
OS Memory 30124.00k
Timestamp 03/30/2018 10:48:35 AM
Step Count 52 Switch Count 2
Page Faults 0
Page Reclaims 143
Page Swaps 0
Voluntary Context Switches 9
Involuntary Context Switches 0
Block Input Operations 0
Block Output Operations 264

94 proc copula;

95 var ret_x ret_y ret_z;
96 define cop normal (cor = estimates);
___
1
WARNING 1-322: Assuming the symbol CORR was misspelled as cor.
97 simulate cop / ndraws = 500
98 outuniform = simulated_uniforms
99 plots=(data=uniform scatter);
____
22
202
ERROR 22-322: Syntax error, expecting one of the following: ), DATATYPE, DISTRIBUTION, NONE.
ERROR 202-322: The option or parameter is not recognized and will be ignored.
100 run;

NOTE: The SAS System stopped processing this step because of errors.
WARNING: The data set WORK.SIMULATED_UNIFORMS may be incomplete. When this step was stopped there were 0 observations and 0
variables.
WARNING: Data set WORK.SIMULATED_UNIFORMS was not replaced because this step was stopped.
NOTE: PROCEDURE COPULA used (Total process time):
real time 0.00 seconds
user cpu time 0.00 seconds
system cpu time 0.00 seconds
memory 339.25k
OS Memory 29864.00k
Timestamp 03/30/2018 10:48:35 AM
Step Count 53 Switch Count 0
Page Faults 0
Page Reclaims 52
Page Swaps 0
Voluntary Context Switches 0
Involuntary Context Switches 0
Block Input Operations 0
Block Output Operations 16

101
102
103 OPTIONS NONOTES NOSTIMER NOSOURCE NOSYNTAXCHECK;
115
Occasional Contributor
Posts: 7

## Joint probably distribution of three variable using copula

I have used this for program for copula simulation

data returns;
input ret_x ret_y ret_z;
cards;
0.004182 0.003503 0.584
-0.027960 -0.000582 0.54
0.006732 0.025611 0.14
-0.033435 -0.002838 -0.24
0.029560 0.010814 -0.4
-0.003054 -0.001689 0.8
-0.012255 -0.012408 0.9
0.013958 0.003427 0.14
-0.011318 -0.017075 0.14
-0.022587 0.002316 0.28
;
/* Copula estimation */
proc copula data = returns;
var ret_x ret_y ret_z;
fit normal / outcopula=estimates;
/* keep only correlation estimates */
data estimates;
set estimates;
keep ret_x ret_y ret_z;
/* Copula simulation */
proc copula;
var ret_x ret_y ret_z;
define cop normal (cor = estimates);
simulate cop / ndraws = 500
outuniform = simulated_uniforms
plots=(data=uniform scatter);
run;

Got this log :

1 OPTIONS NONOTES NOSTIMER NOSOURCE NOSYNTAXCHECK;
70
71 data returns;
72 input ret_x ret_y ret_z;
73 cards;

NOTE: The data set WORK.RETURNS has 10 observations and 3 variables.
NOTE: DATA statement used (Total process time):
real time 0.00 seconds
user cpu time 0.00 seconds
system cpu time 0.00 seconds
memory 521.87k
OS Memory 28840.00k
Timestamp 03/30/2018 10:48:35 AM
Step Count 50 Switch Count 2
Page Faults 0
Page Reclaims 131
Page Swaps 0
Voluntary Context Switches 10
Involuntary Context Switches 0
Block Input Operations 0
Block Output Operations 272

84 ;

85 /* Copula estimation */
86 proc copula data = returns;
87 var ret_x ret_y ret_z;
88 fit normal / outcopula=estimates;
89 /* keep only correlation estimates */

NOTE: The data set WORK.ESTIMATES has 3 observations and 9 variables.
NOTE: PROCEDURE COPULA used (Total process time):
real time 0.04 seconds
user cpu time 0.04 seconds
system cpu time 0.00 seconds
memory 2572.53k
OS Memory 30124.00k
Timestamp 03/30/2018 10:48:35 AM
Step Count 51 Switch Count 2
Page Faults 0
Page Reclaims 517
Page Swaps 0
Voluntary Context Switches 9
Involuntary Context Switches 0
Block Input Operations 0
Block Output Operations 272

90 data estimates;

91 set estimates;
92 keep ret_x ret_y ret_z;
93 /* Copula simulation */

NOTE: There were 3 observations read from the data set WORK.ESTIMATES.
NOTE: The data set WORK.ESTIMATES has 3 observations and 3 variables.
NOTE: DATA statement used (Total process time):
real time 0.00 seconds
user cpu time 0.00 seconds
system cpu time 0.00 seconds
memory 801.06k
OS Memory 30124.00k
Timestamp 03/30/2018 10:48:35 AM
Step Count 52 Switch Count 2
Page Faults 0
Page Reclaims 143
Page Swaps 0
Voluntary Context Switches 9
Involuntary Context Switches 0
Block Input Operations 0
Block Output Operations 264

94 proc copula;

95 var ret_x ret_y ret_z;
96 define cop normal (cor = estimates);
___
1
WARNING 1-322: Assuming the symbol CORR was misspelled as cor.
97 simulate cop / ndraws = 500
98 outuniform = simulated_uniforms
99 plots=(data=uniform scatter);
____
22
202
ERROR 22-322: Syntax error, expecting one of the following: ), DATATYPE, DISTRIBUTION, NONE.
ERROR 202-322: The option or parameter is not recognized and will be ignored.
100 run;

NOTE: The SAS System stopped processing this step because of errors.
WARNING: The data set WORK.SIMULATED_UNIFORMS may be incomplete. When this step was stopped there were 0 observations and 0
variables.
WARNING: Data set WORK.SIMULATED_UNIFORMS was not replaced because this step was stopped.
NOTE: PROCEDURE COPULA used (Total process time):
real time 0.00 seconds
user cpu time 0.00 seconds
system cpu time 0.00 seconds
memory 339.25k
OS Memory 29864.00k
Timestamp 03/30/2018 10:48:35 AM
Step Count 53 Switch Count 0
Page Faults 0
Page Reclaims 52
Page Swaps 0
Voluntary Context Switches 0
Involuntary Context Switches 0
Block Input Operations 0
Block Output Operations 16

101
102
103 OPTIONS NONOTES NOSTIMER NOSOURCE NOSYNTAXCHECK;
115
Super User
Posts: 13,583

## Re: Joint probability distribution of three variable

Multiple identical posts merged to a single topic.

Occasional Contributor
Posts: 7

## Re: Joint probability distribution of three variable

Sorry for the mistake Sir ...thanks a lot for replying ....expecting good answers from the people like you

Solution
‎03-31-2018 04:06 AM
SAS Super FREQ
Posts: 4,245

## Re: Joint probability distribution of three variable

You didn't mention what version of SAS you are running, but here is a link to the most recent doc.

1. The correct syntax for the DEFINE statement is

define cop normal (corr = estimates);

2. The correct syntax for the PLOTS option is

plots=(datatype=uniform);

If you are using an older version of SAS that might have different syntax, consult the documentation for your version.

Occasional Contributor
Posts: 7

## Re: Joint probability distribution of three variable

data returns;
input ret_x ret_y ret_z;
cards;
0.004182 0.003503 0.584
-0.027960 -0.000582 0.54
0.006732 0.025611 0.14
-0.033435 -0.002838 -0.24
0.029560 0.010814 -0.4
-0.003054 -0.001689 0.8
-0.012255 -0.012408 0.9
0.013958 0.003427 0.14
-0.011318 -0.017075 0.14
-0.022587 0.002316 0.28
;
/* Copula estimation and simulation of returns */
proc copula data = returns;
var ret_x ret_y ret_z;
* fit T-copula to stock returns;
fit T /
marginals = empirical
method = MLE
plots = (datatype = both);
* simulate 10000 observations;
* independent in time, dependent in cross-section;
simulate /
ndraws = 10000
seed = 1234
out = simulated_returns
plots(unpack) = (datatype = original);

/* compute equally weighted portfolio return */
data port_ret (drop = i ret);
set simulated_returns;
array returns{3} ret_x ret_y ret_z;
ret =0;
do i =1 to 3;
ret = ret+ 0.2*exp(returns[i]);
end;
port_ret = ret-1;
/* compute descriptive statistics */
/* quantile table will give Value-at-Risk estimates for the portfolio */
proc univariate data = port_ret;
var port_ret;
run;

I have used this code in SAS o demand of academics. its working and got results...Stil I am having one problem..I didnt get a combined JPDF..what i have to do for that
Occasional Contributor
Posts: 7

## Re: Joint probability distribution of three variable

Dear sir,  I have got the following results, but i am expecting a JPDF table, How to get that jpdf

Occasional Contributor
Posts: 7

## Re: Joint probability distribution of three variable

Thanks for your reply sir .. am using Sas on demand of academics ....can i use the syntax suggested by you ?
☑ This topic is solved.