Documentation Center

  • Trials
  • Product Updates

vgxma

Convert VARMA model to VMA model

Synopsis

SpecMA = vgxma(Spec)

SpecMA = vgxma(Spec,nMA,MAlag,Cutoff)

Description

vgxma converts a VARMA model into a pure vector moving average (VMA) 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

nMA

Number of MA lags for the output specification structure. vgxma truncates an infinite-order VMA model to nMA lags. If specific MA lags are not given by MAlag, the lags are 1:nMA. To use MAlag, set nMA to [] or to the number of specific lags.

MAlag

A positive integer vector of specific MA lags for the output specification structure. MAlag must be of length nMA, unless nMA 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 nMA and MAlag.

If neither nMA nor MAlag is specified, vgxma 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 VMA representation (with unit roots close to 1), a large number of initial values is also needed for propagation.

Output Arguments

SpecMA

A transformed multivariate time series specification structure that consists of a pure vector moving average (VMA) model with nMA lags. Logical indicators for model parameter estimation ("solve" information) in Spec are not passed on to SpecMA.

Examples

expand all

Convert a VARMA Model to a VMA Model

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

load Data_VARMA22

Convert Spec into a pure VMA(2) model in SpecMA:

SpecMA = vgxma(Spec);

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

vgxdisp(Spec, SpecMA)
  Model 1: 2-D VARMA(2,2) with No Additive Constant
           Conditional mean is AR-stable and is MA-invertible
  Model 2: 2-D VMA(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                
           (1,2)       0.124043                
           (2,1)       0.375488                
           (2,2)       0.259077                
      AR(2)(1,1)      0.0754758                
           (1,2)     -0.0972418                
           (2,1)      0.0687406                
           (2,2)      0.0155532                
      MA(1)(1,1)       0.205242       0.579177 
           (1,2)      -0.239925      -0.115882 
           (2,1)     -0.0881847       0.287303 
           (2,2)     -0.0617094       0.197368 
      MA(2)(1,1)     -0.0682232       0.259465 
           (1,2)      0.0107276      -0.105364 
           (2,1)      -0.155213       0.205435 
           (2,2)     -0.0040213      0.0191531 
          Q(1,1)           0.08           0.08 
          Q(2,1)           0.01           0.01 
          Q(2,2)           0.03           0.03 

Obtain the first 4 MA lags in SpecMA:

SpecMA = vgxma(Spec, 4);
vgxdisp(Spec, SpecMA);
  Model 1: 2-D VARMA(2,2) with No Additive Constant
           Conditional mean is AR-stable and is MA-invertible
  Model 2: 2-D VMA(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                
           (1,2)       0.124043                
           (2,1)       0.375488                
           (2,2)       0.259077                
      AR(2)(1,1)      0.0754758                
           (1,2)     -0.0972418                
           (2,1)      0.0687406                
           (2,2)      0.0155532                
      MA(1)(1,1)       0.205242       0.579177 
           (1,2)      -0.239925      -0.115882 
           (2,1)     -0.0881847       0.287303 
           (2,2)     -0.0617094       0.197368 
      MA(2)(1,1)     -0.0682232       0.259465 
           (1,2)      0.0107276      -0.105364 
           (2,1)      -0.155213       0.205435 
           (2,2)     -0.0040213      0.0191531 
      MA(3)(1,1)             []       0.138282 
           (1,2)             []     -0.0649623 
           (2,1)             []       0.194931 
           (2,2)             []      -0.039497 
      MA(4)(1,1)             []      0.0754946 
           (1,2)             []      -0.039006 
           (2,1)             []       0.123456 
           (2,2)             []     -0.0415703 
          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:

SpecMA = vgxma(Spec, 1, 99);
vgxdisp(SpecMA);
  Model  : 2-D VMA(1) with No Additive Constant
           Conditional mean is AR-stable and is MA-invertible
           Moving average lags: 99
  MA(99) Moving Average Matrix:
     2.09723e-30   -1.03631e-30 
     3.16333e-30   -8.85453e-31 
  Q Innovations Covariance:
            0.08           0.01 
            0.01           0.03 

See Also

Was this topic helpful?