ARMA {dse1} | R Documentation |
Constructs an ARMA TSmodel object as used by the DSE package.
ARMA(A=NULL, B=NULL, C=NULL, TREND=NULL, description=NULL, names=NULL, input.names=NULL, output.names=NULL) is.ARMA(obj)
A |
The auto-regressive polynomial, an axpxp array. |
B |
The moving-average polynomial, an bxpxp array. |
C |
The input polynomial, an cxpxm array. C should be NULL if there is no input |
TREND |
A matrix, p-vector, or NULL. |
description |
An arbitrary string. |
names |
A list with elements input and output, each a vector of strings. Arguments input.names and output.names should not be used if argument names is used. |
input.names |
A vector of strings. |
output.names |
A vector of strings. |
obj |
Any object. |
The ARMA model is defined by:
A(L)y(t) = B(L)w(t) + C(L)u(t) + TREND(t)
where
The name of last term, TREND
, is misleading. If it is NULL it is treated
as zero. If it is a p-vector, then this constant vector is added to the
the p-vector y(t)
at each period. For a stable model this would give the
none zero mean, and might more appropriately be called the constant or intercept
rather than trend. If the model is for differenced data, then this mean is the
trend of the undifferenced model. The more general case is when TREND
is
a time series matrix of the same dimension as y
. In this case it is added
to y
. This allows for a very general deterministic component, which may
or may not be a traditional trend.
An ARMA TSmodel
mod1 <- ARMA(A=array(c(1,-.25,-.05), c(3,1,1)), B=array(1,c(1,1,1))) AR <- array(c(1, .5, .3, 0, .2, .1, 0, .2, .05, 1, .5, .3) ,c(3,2,2)) VAR <- ARMA(A=AR, B=diag(1,2)) C <- array(c(0.5,0,0,0.2),c(1,2,2)) VARX <- ARMA(A=AR, B=diag(1,2), C=C) MA <- array(c(1, .2, 0, .1, 0, 0, 1, .3), c(2,2,2)) ARMA <- ARMA(A=AR, B=MA, C=NULL) ARMAX <- ARMA(A=AR, B=MA, C=C)