Question

An ARMA(3, 0) model is fit to the following quarterly time series: Year Quarter 1 Quarter 2 Quarter 3 Quarter 4 2018 3.53 1.33 1.85 0.61 2019 0.98 3.61 3.44 3.38 2020 2.91 2.12 4.62 2.93 The estimated coefficients are: ar1 ar2 ar3 intercept 0.252 0.061 -0.202 2.637 Forecast the value for Quarter 1 of 2021. Give full explanation on how you arrived to your answer. Show calculations. A. Less that 3.00 B. At least 3.00, but less than 3.25 C. At least 3.25, but less than 3.50 D. Atleast 3.50, but less than 3.75 E. At least 3.75.

Answer 1

Answer: A. Less that 3.00

Step-by-step explanation:

We will essentially be using a multiple regression formula to predict the value of the first quarter of 2021.

Equation is:

Y₂₀₂₁ = Intercept + ar1X₁ + ar2X₂ + ar3X₃

Y = Quarter 1, 2021

X₁ = Quarter 1, 2018

X₂ = Quarter 1, 2019

X₃ = Quarter 1, 2020

= 2.637 + (0.252 * 3.53) + (0.061 * 0.98) + (-0.202 * 2.91)

= 2.99852

This is less than 3 so the first option is correct.