far.cv {far}

Cross Validation for FARX(1) model

Description

Cross Validation for FAR(1) and FARX(1) models

Usage

far.cv(data, y, x, kn, ncv, cvcrit, center=TRUE, na.rm=TRUE, joined=FALSE)

Arguments

data

A fdata object.

y

A vector giving the name(s) of the endogenous variable(s) of the model.

x

A vector giving the name(s) of the exogenous variable(s) of the model.

kn

A vector giving the maximum values of the various kn (dimension of plug-in in the algorithm). If it not supplied, the number of discretization point is used.

ncv

Number of observations used to the cross validation

cvcrit

A vector of characters. Name of the variable used to measure the errors (y by default).

center

Logical. Does the observation need to be centered.

na.rm

Logical. Does the n.a. need to be removed.

joined

Logical. If TRUE, the joined (whole) far model is computed, otherwise the model work with the separated variables.

Details

In order to perform good forecasting with a FAR or FARX model, you need to determine the dimensions kn of the subspace in which the linear operator is estimated (see far for more details).

This function helps the user to do this choice by performing a cross validation on a test sample. The usage is close of the far function, so we will discuss about the options which differ.

First, the kn option is used to restrict the values searched: this is a vector containing the maxima values. As in far, the dimension of this vector is function of the number of variables involved in the model and the type of estimation done (joined or not).

ncv is the number of observation used to test the models. If it is not provided, the function use the last fifth of the observations in data. In such a case, the four first fifth are used to estimates the models. This is in general a good compromise.

Finally, cvcrit list the variables used to test the models. If more than one variable is provided, the test is calculated as a mean of the errors over all the variables.

The criteria used to test the (functional) errors are the norms L1, L2, L infinite, L1 on the maxima, L2 on the maxima, and L infinite on the maxima.

Value

It is a LIST with the following elements

cv

Matrix giving the various errors (L1, L2, L infinite, L1 on the maxima, L2 on the maxima, L infinite on the maxima) for the tested values of kn

minL1

A vector corresponding to the row of cv where the L1 error minima is obtained

minL2

A vector corresponding to the row of cv where the L2 error minima is obtained

minLinf

A vector corresponding to the row of cv where the L infinite error minima is obtained

minL1max

A vector corresponding to the row of cv where the L1 maxima's error minima is obtained

minL2max

A vector corresponding to the row of cv where the L2 maxima's error minima is obtained

minLinfmax

A vector corresponding to the row of cv where the L infinite maxima's error minima is obtained

Author(s)

J. Damon

See Also

far, fdata

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)

  # Cross validation (joined and separate)
  model1.cv <- far.cv(data=data1, y="X", x="Z", kn=8, ncv=10, cvcrit="X",
                center=FALSE, na.rm=FALSE, joined=TRUE)
  model2.cv <- far.cv(data=data1, y="X", x="Z", kn=c(4,4), ncv=10, cvcrit="X",
                center=FALSE, na.rm=FALSE, joined=FALSE)
  print(model1.cv)
  print(model2.cv)
  k1 <- model1.cv$minL2[1]
  k2 <- model2.cv$minL2[1:2]

  # Modelization of the FARX process (joined and separate)
  model1 <- far(data=data1, y="X", x="Z", kn=k1,
                center=FALSE, na.rm=FALSE, joined=TRUE)
  model2 <- far(data=data1, y="X", x="Z", kn=k2,
                center=FALSE, na.rm=FALSE, joined=FALSE)
  print(model1)
  print(model2)