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:

ScreenHunter_02 Oct. 10 22.16

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

ScreenHunter_03 Oct. 10 22.40

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:

ScreenHunter_09 Oct. 10 22.53

ScreenHunter_11 Oct. 10 22.56

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:

ScreenHunter_12 Oct. 10 23.02

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

ScreenHunter_14 Oct. 10 23.07

Numerical Example: (Coming soon)

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