Random Matrices

Simulate a Vector AR Process

Use MatrixNormalDistribution to simulate the vector autoregressive process.

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sigR = Covariance[ARProcess[{a}, 1][Range[0, 100]]]; sigC = {{s11, s12}, {s12, s22}};
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rules = {a -> 1/2, s11 -> 1, s12 -> 1/2, s22 -> 3};
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\[ScriptCapitalD] = MatrixNormalDistribution[sigR, sigC] /. rules;

Simulate a random sample from the matrix distribution.

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

Construct TemporalData from sampled values.

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td = TemporalData[vals, {0, Length[sigR] - 1, 1}, ValueDimensions -> 2]
Out[5]=

Estimate the diagonal vector autoregressive process.

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proc = ARProcess[{a IdentityMatrix[2]}, sigC];
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sol = FindProcessParameters[td, proc]
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Compare to the original values.

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sol[[All, 2]] - rules[[All, 2]]
Out[8]=

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