coef.far: Extract Model Coefficients

In Looping027/far: Modelization for Functional AutoRegressive Processes

Extract Model Coefficients

Description

'coef' method to extract the linear operator of a FAR model.

Usage

  ## S3 method for class 'far'
coef(object, ...)

Arguments

object	An object of type far.
...	Other arguments (not used in this case).

Details

Give the matricial representation of the linear operator express in the canonical basis. See far for more details about the meaning of this operator.

If the far model is used on a one dimensional variable or with the joined=TRUE option, then the matrix has a dimension equal to the subspace dimension.

In the other case, the dimension of the matrix is equal to the sum of the dimensions of the various subspaces. In such a case, the order of the variables in the matrix is the same as in the vector c(y,x). For instance, if kn=c(3,2) with y="Var1" and x="Var3" then:

• The first 3x3 first bloc of the matrix is the autocorrelation of “Var1”.

• The 3x2 up right bloc of the matrix is the correlation of “Var3” on “Var1”.

• The 2x3 down left bloc of the matrix is the correlation of “Var1” on “Var3”.

• The 2x2 down right bloc of the matrix is the autocorrelation of “Var3”.

Value

A square matrix of size (raw and column) equal to the sum of the element of kn.

Author(s)

J. Damon, S. Guillas

See Also

far,coef

Examples

  # Simulation of a FARX process
  data1 <- simul.farx(m=10,n=400,base=base.simul.far(20,5),
                base.exo=base.simul.far(20,5),
                d.a=matrix(c(0.5,0),nrow=1,ncol=2),
                alpha.conj=matrix(c(0.2,0),nrow=1,ncol=2),
                d.rho=diag(c(0.45,0.90,0.34,0.45)),
                alpha=diag(c(0.5,0.23,0.018)),
                d.rho.exo=diag(c(0.45,0.90,0.34,0.45)),
                cst1=0.0)

  # Modelization of the FARX process (joined and separate)
  model1 <- far(data1,kn=4,joined=TRUE)
  model2 <- far(data1,kn=c(3,1),joined=FALSE)

  # Calculation of the theoretical coefficients
  coef.theo <- theoretical.coef(m=10,base=base.simul.far(20,5),
                base.exo=base.simul.far(20,5),
                d.a=matrix(c(0.5,0),nrow=1,ncol=2),
                alpha.conj=matrix(c(0.2,0),nrow=1,ncol=2),
                d.rho=diag(c(0.45,0.90,0.34,0.45)),
                alpha=diag(c(0.5,0.23,0.018)),
                d.rho.exo=diag(c(0.45,0.90,0.34,0.45)),
                cst1=0.0)

  # Joined coefficient
  round(coef(model1),2)
  coef.theo$rho.T

  # Separate coefficient
  round(coef(model2),2)
  coef.theo$rho.X.Z

Looping027/far documentation built on Aug. 15, 2022, 7:15 a.m.