Question

Using a sample of 50 quarters of inflation data, you carry out an AR(2) model regression, and produce the following results:

	Coefficient	Standard error
Intercept	1.77	0
Inflation t-1	0.12	0.01
Inflation t-2	0.12	0.02

The two most recent quarterly annualized inflation observations in your data are 2.03 (second to last observation) and 2.18 (latest observation).

Based on these results, what is your prediction for the rate of inflation at time 52 (two quarters in the future from your latest observation)?

Please show on excel.

The answer is 2.3

Answer 1

Following is screenshot of calculation done in MS Excel:

Below is the explanation of calculation done by hand:

In this case, following data is given:

Inflation₅₀ = Y₅₀ = 2.18

Inflation₄₉ = Y₄₉ =2.03

Equation for AR(2) model is given as:

Y_t = b₀ + b₁*Y_t-1 + b₂*Y_t-2

From the table it can be seen that b₀ = 1.77, b₁ = 0.12 and b₂ = 0.12

So, equation for AR(2) model can be written as:

Y_t = 1.77 + 0.12*Y_t-1 + 0.12*Y_t-2

Now, we need to find Y₅₂

Y₅₂ = 1.77 + 0.12*Y_52-1 + 0.12*Y_52-2

Y₅₂ = 1.77 + 0.12*Y₅₁ + 0.12*Y₅₀

Now, we know that Y₅₀ = 2.18, but we need to find Y₅₁

Again using the equation for AR(2) model, we get:

Y₅₁ = 1.77 + 0.12*Y_51-1 + 0.12*Y_51-2

Y₅₁ = 1.77 + 0.12*Y₅₀ + 0.12*Y₄₉

Substituting the value of Y₅₀ and Y₄₉ in the above equation, we get:

Y₅₁ = 1.77 + 0.12*2.18 + 0.12*2.03

Y₅₁ = 2.2752

Substituting the value of Y₅₁ and Y₅₀ in the equation derived for Y₅₂, we get

Y₅₂ = 1.77 + 0.12*2.2752 + 0.12*2.18

Y₅₂ = 2.30