Question4,page5-7An investment consultant firm believes that its operation profit is strongly influenced by the volume of shares traded on the New York Stock Exchange (NYSE). Two analysts are hired to model the volume series. The monthly log volume of the NYSE and its change (difference) are plotted in the diagrams below.(a) One analyst has estimated three models from 537 monthly observations onthe differenced log volume of the NYSE, {?yt}. The estimation results are summarized in the table below, where ?yt is the dependent (or left hand side) variable. Estimation Results Model ?yt-1 ?yt-2 ?yt-3 et-1 c SSR AR(2) -.413 -.218 .016 16.94 [.042] [.042] [.008] AR(3) -.414 -.220 -.005 .016 16.94 [.043] [.046] [.043] [.008] ARMA(1,1) .346 -.794 .007 16.35 [.066] [.043] [.002] The standard errors for estimated coefficients are given in brackets.(i) Based on the above table, which model would you prefer? Explain briefly. [4 marks](ii) Regardless of your answer to (i), use the estimated AR(2) model to make 1-step ahead and 2-step ahead point forecasts for the differenced log volume. It is known that the most recent observations ?yT = .23 and ?yT -1 = -.15. [4 marks](b) The other analyst has estimated two models from 537 monthly observations on the log volume of the NYSE, {yt}. The estimation results are summarized below, where the difference ?yt = yt – yt-1 is the dependent variable. Estimation Results Model yt-1 ?yt-1 ?yt-2 t c SSR Model A -.141 -.325 -.165 .00147 .391 16.20 [.029] [.045] [.043] [.00030] [.078] Model B -.413 -.218 .00001 .013 16.94 [.042] [.042] [.00005] [.016] The standard errors for estimated coefficients are given in brackets.Based on the above table, should yt-1 be included in the model? Explain briefly. [4 marks](c) Given the models in (a) and (b), Comment on whether or not a combination of the forecasts from different models may improve forecast performance in this context. [3 marks]