3. Suppose that the Gross Domestic Product (GDP) in the US in denoted as " . Let the quarterly data of ", from 1980:1 to 2015:1 is non-stationary but the

3. Suppose that the Gross Domestic Product (GDP) in the US in denoted as "
. Let the quarterly data of ", from 1980:1 to 2015:1 is non-stationary but
the first difference of" , denoted as ,, is stationary. Assume that a
researcher identified the following AR model for DG, :
DG, =Q, +a, DG,_, +a, DG,_; +a,DG,_. +e,
Suppose the estimated results of the above AR model are as follows:
DG, = 6.09+0.18DG,_, + 0.12DG,_, + 0.05DG,_4
(a) Based on what criteria of the coefficients of auto-correlation function
(ACF) and the coefficients of partial auto-correlation function (PACF),
the researcher identified the above AR model? Explain. Also explain why
the researcher chose 1, 3, and 4 lags. (10)
(b) Forecast the GDP for 2015:2, assuming that the GDP in 2015:1, 2014:4,
2014:3, 2014:2, 2014:1, 2013:4, 2013:3, and 2013:2 respectively are:
16264.1, 16294.7, 16205.6, 16010.4, 15831.7, 15916.2,15779.9, and
15606.6. (20)
() Explain how to conduct a diagnostic test to check if the researcher has
identified the correct AR model. (nt: Step 3 of Box-Jenkin’s Method)
(10)

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