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Create and Adjust VAR Model Using Shorthand Syntax

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This example shows how to create a three-dimensional VAR(4) model with unknown parameters using varm and the shorthand syntax. Then, this example shows how to adjust parameters of the created model using dot notation.

Create a VAR(4) model for a three-dimensional response series using the shorthand syntax.

numseries = 3;
p = 4;
Mdl = varm(3,4)
Mdl = 
  varm with properties:

     Description: "3-Dimensional VAR(4) Model"
     SeriesNames: "Y1"  "Y2"  "Y3" 
       NumSeries: 3
               P: 4
        Constant: [3×1 vector of NaNs]
              AR: {3×3 matrices of NaNs} at lags [1 2 3 ... and 1 more]
           Trend: [3×1 vector of zeros]
            Beta: [3×0 matrix]
      Covariance: [3×3 matrix of NaNs]

Mdl is a varm model object. The properties of the model display at the command line. Observe that:

  • The default value of some of the parameters are NaN values, which indicates their presence in the model. In particular, each lag from 1 through 4 has an unknown, nonzero autoregressive coefficient matrix.

  • You created the model without using response data. That is, Mdl is agnostic about data.

Suppose that you want lags 1 and 4 in the model to be unknown and nonzero, but all other lags are zero. Using dot notation, remove the other lags from the model object by placing 3-by-3 matrices of zeros the corresponding cells.

Mdl.AR{2} = zeros(3);
Mdl.AR{3} = zeros(3)
Mdl = 
  varm with properties:

     Description: "3-Dimensional VAR(4) Model"
     SeriesNames: "Y1"  "Y2"  "Y3" 
       NumSeries: 3
               P: 4
        Constant: [3×1 vector of NaNs]
              AR: {3×3 matrices} at lags [1 4]
           Trend: [3×1 vector of zeros]
            Beta: [3×0 matrix]
      Covariance: [3×3 matrix of NaNs]

Observe that the model degree p is still 4, but there are unknown, nonzero coefficients at lags 1 and 4 only.

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