Vector Autoregression Model and Matrix Algebra: The Federal Reserve’s Monetary Target Barometer

Federal Reserve Seal

Historical Notes and Applications: (coming soon)

Mathematical Model:

These are the primitive equations in the Vector Autoregression Model (VAR)

Primitive Equations:

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Next, write the above equations in matrix-vector notation:

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To simplify the notation and calculations the following substitutions and notations will be generated:

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The substitutions into can help write equation 1 and 2 in matrix-vector notation:

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The formula for the vector x is composed of the the formula for B inverse, including this formula for the inverse in our calculations we get the final version of the vector x in the Vector Autoregression Model:

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Using the above formula for the inverse of be we get the final vector:

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Numerical Example: (Coming soon)