2. Suppose observations y, follow a trend + season time series model: y1 = Ti+ Site Et ~ N(0, 57 ) (a) Suppose we fit a linear trend To = Po + 81TIME, and neglected the seasonal component St. Also assume the trend is not miss specified, that is, To = Bo + 81TIME. Show the regression residual given by et = y: - yt is exactly the missing seasonal component S. (10 points). (b) Explain why this should motivate us to always look into regression residual plots. (5 points) (c) Suppose we now take seasonality into account. The period of seasonality is 4 and sample size is 7 = 60. We estimate the following parameters: B2 = 2 M1 = 1 12 = 2 13 = 1 54 = 0 83 = 4 Provide point-forecasts, density forecasts and 68% confidence interval forecasts at T + h = 63