dse (version 2020.2-1)

ARMA: 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, 
          constants=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.

constants

NULL or a list of logical arrays with the same names as arrays above, indicating which elements should be considered constants.

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.

Value

An ARMA TSmodel

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.

This is sometime called a vector ARMA (VARMA) model, but the univariate case is also handled by this structure. VAR models are a special case where B(L) = I. ARIMA models are also special cases where the polynomial arrays have unit roots, but these are not distinguished in a separate term as is sometimes done in other programs.

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.

By default, elements in parameter arrays are treated as constants if they are exactly 1.0 or 0.0, and as parameters otherwise. A value of 1.001 would be treated as a parameter, and this is the easiest way to initialize an element which is not to be treated as a constant of value 1.0. Any array elements can be fixed to constants by specifying the list constants. Arrays which are not specified in the list will be treated in the default way. An alternative for fixing constants is the function fixConstants.

The function ARMA sets up a model but does not estimate it. See estVARXls for one possibility for estimating VAR models and estMaxLik for one possibility for estimating ARMA models.

See Also

TSmodel, simulate.ARMA, fixConstants estVARXls estMaxLik

Examples

# NOT RUN {
    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) 
# }