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. (Hint: Step 3 of Box-Jenkin's Method)