Simulate a Vector AR Process: New in Wolfram Language 11

Simulate a Vector AR Process

Use MatrixNormalDistribution to simulate the vector autoregressive process.

In[1]:=

sigR = Covariance[ARProcess[{a}, 1][Range[0, 100]]];
sigC = {{s11, s12}, {s12, s22}};

In[2]:=

rules = {a -> 1/2, s11 -> 1, s12 -> 1/2, s22 -> 3};

In[3]:=

\[ScriptCapitalD] = MatrixNormalDistribution[sigR, sigC] /. rules;

Simulate a random sample from the matrix distribution.

In[4]:=

vals = RandomVariate[\[ScriptCapitalD], 10^4];

Construct TemporalData from sampled values.

In[5]:=

td = TemporalData[vals, {0, Length[sigR] - 1, 1}, 
  ValueDimensions -> 2]

Out[5]=

Estimate the diagonal vector autoregressive process.

In[6]:=

proc = ARProcess[{a IdentityMatrix[2]}, sigC];

In[7]:=

sol = FindProcessParameters[td, proc]

Out[7]=

Compare to the original values.

In[8]:=

sol[[All, 2]] - rules[[All, 2]]

Out[8]=