SMC Procedure
AUXMODEL Statement
AUXMODEL dependent-variable ~ distribution;
The AUXMODEL statement specifies the auxiliary conditional distribution of the dependent variable given the parameters, the lagged state variables, the lagged dependent variables, and the independent variables; that is, 
, 
. For more information about the auxiliary conditional distribution in the state space model, see the section Auxiliary Particle Filter.
The AUXMODEL statement is ignored if you specify the SUBMITMODEL statement. The AUXMODEL statement has the following requirements if you omit the SUBMITMODEL statement:
If you specify the ALGORITHM=APF option in the EVALUATE, FILTER, FORECAST, LEARN, or SMOOTH statement, each dependent variable must have a corresponding AUXMODEL statement.
Multiple AUXMODEL statements are permitted.
The AUXMODEL statement must have the following components in the order shown:
Dependent variable: A single dependent variable from the input data table.
Tilde: A tilde (~) symbol between the dependent variable and the distribution.
-
Distribution: A distribution that is specified in the form distribution-name(distribution-arguments). The available distribution-name and distribution-arguments in the AUXMODEL statements are displayed in Table 2. For the description of each distribution, see the section Standard Distributions.
Table 2: Distribution Names and Arguments
Distribution Name Distribution Arguments Definitions BETA a, b Beta distribution with arguments shape parameter a and shape parameter b CAUCHY l, s Cauchy distribution with arguments location l and scale s GAMMA a, b Gamma distribution with arguments shape a and scale b LOGN m, s Log-normal distribution with arguments mean m and standard deviation s NORMAL | N m, s Normal distribution with arguments mean m and standard deviation s POISSON 
Poisson distribution with argument mean
T m, s, 
Student’s —t distribution with arguments mean m, standard deviation s, and degrees of freedom
UNIFORM l, u Uniform distribution with arguments min l and scale u
The distribution-arguments are specified by expressions that are enclosed in parentheses and separated by commas. Such expressions must follow any SAS programming statements. To avoid the possible computation errors, you should make some adjustments to the expressions. For more information about the adjustments, see the section Distribution Argument Restriction. The number of expressions is equal to the number of arguments of the given distribution. For the AUXMODEL statement, the variables that can appear in the expressions must be selected from the following list:
the model parameters
the lagged state variables
the lagged dependent variables
the current and lagged independent variables
the actual time index,
_time
For more information about the actual time index, see the section Time Index. For more information about the parameters, state variables, and dependent/independent variables, see the sections PARAMETERS Statement, STATEVAR Statement, and VAR Statement, respectively.
Moreover, the following conditions must be satisfied in the AUXMODEL statement:
The maximum lag order of all the state variables in the distribution-arguments of all AUXMODEL statements must be less than or equal to r, where r is defined in the section Method 1: Maximum Lag Order of State Variables, r.
The maximum lag order of all the dependent variables in the distribution-arguments of all AUXMODEL statements must be less than or equal to p, where p is defined in the section Method 1: Maximum Lag Order of Dependent Variables, p.
The maximum lag order of all the independent variables in the distribution-arguments of all AUXMODEL statements must be less than or equal to s, where s is defined in the section Method 1: Maximum Lag Order of Independent Variables, s.
The dependent variables in all AUXMODEL statements must not have duplicates; that is, each dependent variable should appear only once as the dependent-variable in all AUXMODEL statements.
For example, suppose that the auxiliary distributions of the dependent variables 
and 
are described in the following equations:
Then the following statements define these auxiliary distributions:
auxmodel y1 ~ normal(0, exp(phi * x1.l1/2));
auxmodel y2 ~ normal(beta*x2.l1, gamma);
where phi, beta, and gamma are model parameters; y1 and y2 are current dependent variables; and x1.l1 and x2.l1 are the first-order lagged state variables, which are constructed by appending the suffix ".11" to the state variables "x1" and "x2" (see the section Method 1: Lagged Variables).