# coef.far: Extract Model Coefficients In far: Modelization for Functional AutoRegressive Processes

## Description

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

## Usage

 ```1 2``` ``` ## 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

`far`,`coef`
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31``` ``` # 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 ```