(b) Density forecasts are more informative than interval forecasts. (5 points) (c) The time series model y, =3 , + _; Y;D; + , can be estimated by Ordinary Least Squares . (5 points ) (d) SIC is an adequate model selection criteria to select between quadratic and log linear (log (y ) . = B 1+3 2TIME, + ,) trends . (5 points ) (e) A high adjusted R-square ensures the model will perform well in out -of-samples forecasts . (5 points ) 2. Suppose observations y, follow a trend + season time series model : yt = T+ + S+ + t + ~ N ( 0 , 0 2 ) (a ) Suppose we fit a linear trend T. = B . +8 1TIME, and neglected the seasonal component St . Also assume the trend is not miss specified , that is, T. =3 , +8 TIME,. Show the mean E() of the regression residual, given by et = yt - yt, is exactly the missing seasonal component St. (10 points ). (b) Explain why this should motivate us to always look into regression residual plots. (5 points)