ARMA {dse1}R Documentation

ARMA Model Constructor

Description

Constructs an ARMA TSmodel object as used by the DSE package.

Usage

    ARMA(A=NULL, B=NULL, C=NULL, TREND=NULL, description=NULL,
          names=NULL, input.names=NULL, output.names=NULL)
    is.ARMA(obj)

Arguments

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.

Details

The ARMA model is defined by:

A(L)y(t) = B(L)w(t) + C(L)u(t) + TREND(t)

where

A
(axpxp) is the auto-regressive polynomial array.
B
(bxpxp) is the moving-average polynomial array.
C
(cxpxm) is the input polynomial array. C should be NULL if there is no input
y
is the p dimensional output data.
u
is the m dimensional control (input) data.
TREND
is a matrix the same dimension as y, a p-vector (which gets replicated for each time period), or NULL.

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.

Value

An ARMA TSmodel

See Also

TSmodel simulate.ARMA

Examples

    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) 

[Package dse1 version 2005.1-1 Index]