define.model {marima}

define.model

Description

Function to define multivariate arma model (indicator form) for marima.

Usage

define.model(kvar = 1, ar = 0, ma = 0, rem.var = 0, reg.var = 0,
  no.dep = NULL, print = 0, ar.fill = NULL, ar.rem = NULL,
  ma.fill = NULL, ma.rem = NULL, indep = NULL)

Arguments

kvar

dimension of time series

ar

autoregresssion definition. For example ar=c(1, 2, 12) will generate autoregression at lags 1, 2 and 12.

ma

moving average definition. Works like ar. If ma=c(1, 2) moving average terms at lags 1 and 2 are defined.

rem.var

no. of variable(s) not to be considered in marima.

reg.var

no. of variable(s) that can only act as regression variable(s) such as (typically) a socalled leading indicator.

no.dep

sequence of pairs of variables. For example no.dep=c(1, 2, 2, 3) means that variable 2 is not allowed in model for variable 1, and variable 3 is not allowed in model for variable 2.

print

(!0/0) If !0 is used, the generated patterns of the arma model and other informations are printed on the console. If 0 is used, no printout of the arma patterns are given.

ar.fill

sequence of triplets: c(dependent variable, independent variable, lag). ar.fill=c(2, 3, 12): Insert ar-indicator for model for dependent variable 2 and independent variable 3 at lag 12.

ar.rem

sequence of triplets c(dependent variable, independent variable, lag). ar.rem=c(2, 3, 12): remove (if present) ar-indicator for model for dependent variable 2 and independent variable 3 at lag 12.

ma.fill

sequence of triplets: c(dependent variable, independent variable, lag). ma.fill=c(2, 3, 12): Insert ma-indicator for model for dependent variable 2 and independent variable 3 at lag 12.

ma.rem

sequence of triplets c(dependent variable, independent variable, lag). ma.rem=c(2, 3, 12): remove (if present) ma-indicator for model for dependent variable 2 and independent variable 3 at lag 12.

The various parameters may (in some cases) accomplish the same model requirements. The routine define.model apply these input parameters successively in the following order: 1) rem.var, 2) reg.var, 3) indep, 4) no.dep, 5) ar.fill, 6) ar.rem, 7) ma.fil, 8) ma.rem

The parameters ar.fill, ar.rem, ma.fill and ma.rem are applied last, and in that order. They overwrite what previously has been defined.

indep

no. of variable(s) that are independent of the other variables. indepc(2, 4) makes variables 2 and 4 independent of all other variables. Variables 2 and 4 may influence other variables.

Value

ar.pattern a matrix polynomium (an array) with 1's and 0's defining the autoregressive matrix polynomium to be fitted by marima (an array with dim=c(kvar, kvar, 1+ar_order) (with leading unity matrix)).

ma.pattern a matrix polynomium (an array) with 1's and 0's defining the moving average matrix polynomium to be fitted by marima (an array with dim=c(kvar, kvar, 1+ma_order) (including the leading unity matrix)).

Examples

#
# Example 1: 3-variate arma model with ar-lags at 1 and 2, and an
# ma-term at lag 1. And var=3 is a regression variable (X-variable).
#
 Model1 <- define.model(kvar=3, ar=c(1, 2), ma=c(1), reg.var=3)
 short.form(Model1$ar.pattern)
 short.form(Model1$ma.pattern, leading=FALSE)
#
# The object Model1 contains the ar- and ma-pattern arrays as defined.
#
# Model1$ar.pattern and Model1$ma.pattern are used as input to
# marima in order to define the model to be estimated.
#
# Example 2: arma model with ar-lags at 1, 2 and 6, and var=3
#  regression variable (X-variable).
#
 Model2 <- define.model(kvar=3, ar=c(1, 2, 6), ma=c(1), reg.var=3)
# Print the ar- and ma-polynomial patterns using
 short.form(Model2$ar.pattern, leading=FALSE)
 short.form(Model2$ma.pattern, leading=TRUE)
#
# Example 3: arma model with ar-lags at 1, 2 and 6, and reg.var=3
# (X-variable). ma-order=1. Finally (ar.fill=c(2, 3, 4) puts  a '1'
# for (dep-var=2, indep-var=3, ar-lag=4).
#
# If further modifications of the ar- or ma-patterns are needed, it
# can be accomplished before calling marima (Model3$ar.pattern and
# Model3$ma.pattern are arrays).
#
 Model3 <- define.model(kvar=3, ar=c(1, 2, 6), ma=c(1), reg.var=3,
    ar.fill=c(2, 3, 4))
 short.form(Model3$ar.pattern)
 short.form(Model3$ma.pattern)
#
 Model4 <- define.model(kvar=3, ar=c(1, 2, 6), ma=c(1), reg.var=3, 
 ar.fill=c(2, 3, 4), indep=c(1))
 short.form(Model4$ar.pattern)
 short.form(Model4$ma.pattern, leading=FALSE)