vgxdisp - Display multivariate time series model parameters and standard errors in different formats

Syntax

vgxdisp(Spec) vgxdisp(Spec,'Name1',Value1,'Name2',Value2,...) vgxdisp(SpecStd) vgxdisp(SpecStd,'Name1',Value1,'Name2',Value2,...) vgxdisp(Spec,SpecStd) vgxdisp(Spec,SpecStd,'Name1',Value1,'Name2',Value2,...) vgxdisp(Spec1,Spec2) vgxdisp(Spec1Std,Spec2Std) vgxdisp(Spec1Std,Spec2Std,'Name1',Value1,'Name2',Value2,...) vgxdisp(Spec1,Spec1Std,Spec2,Spec2Std) vgxdisp(Spec1,Spec2,Spec1Std,Spec2Std) vgxdisp(Spec1,Spec1Std,Spec2,Spec2Std,varargin) vgxdisp(Spec1,Spec2,Spec1Std,Spec2Std,'Name1',Value1,'Name2',Value2,...)

Description

vgxdisp displays multivariate time series model parameters and standard errors in different formats.

vgxdisp(Spec) displays a single specification structure Spec.
vgxdisp(Spec,'Name1',Value1,'Name2',Value2,...)
vgxdisp(SpecStd) displays a single standard-error structure SpecStd with no t-statistics.
vgxdisp(SpecStd,'Name1',Value1,'Name2',Value2,...)
vgxdisp(Spec,SpecStd) displays a single specification structure SpecStd with standard errors.
vgxdisp(Spec,SpecStd,'Name1',Value1,'Name2',Value2,...)
vgxdisp(Spec1,Spec2) displays two specification structures Spec1 and Spec2 side-by-side. This option displays the specification structures in table format only.
vgxdisp(Spec1Std,Spec2Std) displays two standard-error structures Spec1Std and Spec2Std side-by-side. This option displays the standard-error structures in table format only.
vgxdisp(Spec1Std,Spec2Std,'Name1',Value1,'Name2',Value2,...)
vgxdisp(Spec1,Spec1Std,Spec2,Spec2Std) or vgxdisp(Spec1,Spec2,Spec1Std,Spec2Std) displays two specification structures side-by-side with standard errors. This option displays the specification structures in table format only.
vgxdisp(Spec1,Spec1Std,Spec2,Spec2Std,varargin) or vgxdisp(Spec1,Spec2,Spec1Std,Spec2Std,'Name1',Value1,'Name2',Value2,...)

Required Input Arguments

`Spec`	A multivariate time series specification structure for an n-dimensional time series process, as created by `vgxset`.
`SpecStd`	A multivariate time series specification structure that contains standard errors (or estimation errors) of estimated parameters for a companion n-dimensional time series process, as created by `vgxset`. Since the standard errors are maximum likelihood estimates, set the parameter `DoFAdj` to `true` to apply a degree-of-freedom adjustment and report ordinary least squares estimates.

If you input multiple specification structures, all must have the same dimension n. Pairs of specification structures and standard errors must be conformable. You can, however, specify different AR or MA lag structures for multiple specification structures, and if the inputs are exogenous, you can also specify different numbers of parameters.

If the specification structures do not set any logical indicators for model parameter estimation ("solve" information), vgxdisp assumes that every parameter is available for estimation. In this case, the degree-of-freedom adjustment that vgxdisp makes is the most conservative estimate for standard errors.

Optional Input Arguments

Specify the following optional input arguments as variable-length lists of matching parameter name/value pairs: 'Name1', Value1, 'Name2', Value2, ... and so on. The following rules apply when specifying parameter-name pairs:

Specify the parameter name as a character string, followed by its corresponding parameter value.
You can specify parameter name/value pairs in any order.
Parameter names are case insensitive.
You can specify unambiguous partial string matches.

The following table lists valid parameter names.

DoFAdj

Specifies whether vgxdisp adjusts for degrees of freedom in standard errors. Options are:

true — vgxdisp applies degree-of-freedom adjustment (least-squares estimation).
false — vgxdisp does not apply degree-of-freedom adjustment (maximum likelihood estimation).

Format

Specifies format in which model parameters and standard errors are displayed. Options are:

'equation' — vgxdisp displays model parameters and standard errors in canonical equation form. This is the default format for single models.
'table' — vgxdisp displays model parameters and standard errors in tabular form. This is the only option for multiple models.

Example

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

load vgxexample Spec EstSpec EstSpecStd

vgxdisp(Spec);

Model - Information
  Model:  2-D VARMA(2,2) with No Additive Constant
          Conditional mean is AR-stable and is MA-invertible

  AR(1) Autoregression Matrix:
        0.373935       0.124043 
        0.375488       0.259077 
  AR(2) Autoregression Matrix:
       0.0754758     -0.0972418 
       0.0687406      0.0155532 
  MA(1) Moving Average Matrix:
        0.205242      -0.239925 
      -0.0881847     -0.0617094 
  MA(2) Moving Average Matrix:
      -0.0682232      0.0107276 
       -0.155213     -0.0040213 
  Q Innovations Covariance:
            0.08           0.01 
            0.01           0.03

Assume that you have a 2-dimensional VAR(2) approximation of the original VARMA(2, 2) model estimated from time series data that is in the specification structure EstSpec:

vgxdisp(Spec, EstSpec);

Model 1 - Information
  Model : 2-D VARMA(2,2) with No Additive Constant
          Conditional mean is AR-stable and is MA-invertible
Model 2 - Information
  Model : 2-D VAR(2) with No Additive Constant
          Conditional mean is AR-stable

     Parameter        Model 1        Model 2
  -------------- -------------- --------------
      AR(1)(1,1)       0.373935       0.850166 
           (1,2)       0.124043     -0.0498191 
           (2,1)       0.375488       0.219381 
           (2,2)       0.259077     -0.0227752 
      AR(2)(1,1)      0.0754758      -0.294609 
           (1,2)     -0.0972418       0.221336 
           (2,1)      0.0687406       0.264504 
           (2,2)      0.0155532      0.0819125 
      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       0.051844 
          Q(2,1)           0.01     0.00711775 
          Q(2,2)           0.03      0.0286081

The estimated VAR(2) model has standard errors for the parameter estimates in EstSpecStd which can be displayed with the estimated model:

vgxdisp(EstSpec, EstSpecStd);

Model - Parameters and Standard Errors
  Model:  2-D VAR(2) with No Additive Constant
   Conditional mean is AR-stable
 Standard errors without DoF adjustment (maximum likelihood)

     Parameter          Value     Std. Error    t-Statistic
  -------------- -------------- -------------- --------------
    AR(1)(1,1)       0.850166        0.12583        6.75649 
         (1,2)     -0.0498191       0.163542      -0.304625 
         (2,1)       0.219381      0.0934711        2.34705 
         (2,2)     -0.0227752       0.121486      -0.187472 
    AR(2)(1,1)      -0.294609       0.145514       -2.02461 
         (1,2)       0.221336       0.148174        1.49376 
         (2,1)       0.264504       0.108094        2.44699 
         (2,2)      0.0819125       0.110069        0.74419 
        Q(1,1)       0.051844                
        Q(2,1)     0.00711775                
        Q(2,2)      0.0286081

vgxcount

vgxget

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