Documentation

vgxar

Convert VARMA model to VAR model

Synopsis

SpecAR = vgxar(Spec)

SpecAR = vgxar(Spec,nAR,ARlag,Cutoff)

Description

vgxar converts a VARMA model into a pure vector autoregressive (VAR) model. This function works only for VARMA models and does not handle exogenous variables (VARMAX models).

Required Input Argument

Spec

A multivariate time series specification structure for an n-dimensional VARMA time series process, as created by vgxset.

Optional Input Arguments

nAR

Number of AR lags for the output specification structure. vgxar truncates an infinite-order VAR model to nAR lags. If specific AR lags are not given by ARlag, the lags are 1:nAR. To use ARlag, set nAR to [] or to the number of specific lags.

ARlag

A positive integer vector of specific AR lags for the output specification structure. ARlag must be of length nAR, unless nAR is [].

Cutoff

The cutoff for the infinity norm below which trailing lags are removed. The default is 0, which does not remove any lags and uses the values for nAR and ARlag.

If neither nAR nor ARlag is specified, vgxar uses the maximum lags of the AR or MA lags of the input Spec.

    Note:   If a large number of lags is needed to form a pure VAR representation (with unit roots close to 1), a large number of initial values is also needed for propagation.

Output Arguments

SpecAR

A transformed multivariate time series specification structure that consists of a pure vector autoregressive (VAR) model with nAR lags. Logical indicators for model parameter estimation ("solve" information) in Spec are not passed on to SpecAR.

Examples

Convert a VARMA Model to a VAR Model

Start with a 2-dimensional VARMA(2, 2) specification structure in Spec:

load Data_VARMA22

Convert Spec into a pure VAR(2) model in SpecAR:

SpecAR = vgxar(Spec);

Display the original specification structure in Spec and compare with the new specification structure in SpecAR:

vgxdisp(Spec, SpecAR)
  Model 1: 2-D VARMA(2,2) with No Additive Constant
           Conditional mean is AR-stable and is MA-invertible
  Model 2: 2-D VAR(2) with No Additive Constant
           Conditional mean is AR-stable and is MA-invertible
       Parameter        Model 1        Model 2
  -------------- -------------- --------------
      AR(1)(1,1)       0.373935       0.579177 
           (1,2)       0.124043      -0.115882 
           (2,1)       0.375488       0.287303 
           (2,2)       0.259077       0.197368 
      AR(2)(1,1)      0.0754758     -0.0426874 
           (1,2)     -0.0972418      -0.015377 
           (2,1)      0.0687406     -0.0176683 
           (2,2)      0.0155532      0.0134923 
      MA(1)(1,1)       0.205242                
           (1,2)      -0.239925                
           (2,1)     -0.0881847                
           (2,2)     -0.0617094                
      MA(2)(1,1)     -0.0682232                
           (1,2)      0.0107276                
           (2,1)      -0.155213                
           (2,2)     -0.0040213                
          Q(1,1)           0.08           0.08 
          Q(2,1)           0.01           0.01 
          Q(2,2)           0.03           0.03 

Instead of just the default number of AR lags (which is two), obtain the first four AR lags in SpecAR:

SpecAR = vgxar(Spec, 4);
vgxdisp(Spec, SpecAR)
  Model 1: 2-D VARMA(2,2) with No Additive Constant
           Conditional mean is AR-stable and is MA-invertible
  Model 2: 2-D VAR(4) with No Additive Constant
           Conditional mean is AR-stable and is MA-invertible
       Parameter        Model 1        Model 2
  -------------- -------------- --------------
      AR(1)(1,1)       0.373935       0.579177 
           (1,2)       0.124043      -0.115882 
           (2,1)       0.375488       0.287303 
           (2,2)       0.259077       0.197368 
      AR(2)(1,1)      0.0754758     -0.0426874 
           (1,2)     -0.0972418      -0.015377 
           (2,1)      0.0687406     -0.0176683 
           (2,2)      0.0155532      0.0134923 
      AR(3)(1,1)             []      0.0409534 
           (1,2)             []    -0.00362997 
           (2,1)             []      0.0861962 
           (2,2)             []     -0.0177161 
      AR(4)(1,1)             []     0.00955252 
           (1,2)             []    -0.00469931 
           (2,1)             []      0.0022339 
           (2,2)             []    -0.00374581 
      MA(1)(1,1)       0.205242                
           (1,2)      -0.239925                
           (2,1)     -0.0881847                
           (2,2)     -0.0617094                
      MA(2)(1,1)     -0.0682232                
           (1,2)      0.0107276                
           (2,1)      -0.155213                
           (2,2)     -0.0040213                
          Q(1,1)           0.08           0.08 
          Q(2,1)           0.01           0.01 
          Q(2,2)           0.03           0.03 

Obtain just the 99th lag and display the result:

SpecAR = vgxar(Spec, 1, 99);
vgxdisp(SpecAR);
  Model  : 2-D VAR(1) with No Additive Constant
           Conditional mean is AR-stable and is MA-invertible
           Autoregression lags: 99
  AR(99) Autoregression Matrix:
     8.06035e-45   -2.39247e-45 
     1.44771e-44   -4.29698e-45 
  Q Innovations Covariance:
            0.08           0.01 
            0.01           0.03 

See Also

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