TIME SERIES AND TIME SERIES

(i) Give the value of the angularfrequency a) which accounts for the seasonality exhibited. {2} {ii} Write down the estimated model in Table 5.1. {3) {iii} Taking into account both the seasonality and trend components find the transformed forecasts for both January and February of 2005, Le. Z; (3?) and Zr (38) and their re- spective prediction limits. {4] (Hint: :3? = [1 3? gimme} cos(3?%}]'). (iv) Taking into account both the seasonality and trend components. nd the minimum mean square error forecast in the original series forecasts for both January and February of 2000, is Y; {3?} and 1G (38) and their respective prediction limits. {6] (Hint: The minimum mean square error forecast is given by exp {2: U} + %Vor[en[i'}]], where Var[en[1]] = 3'2 = 0.1212}, see page 203 of prescribed book). Question 6 The time series plot in the following graph shows Discount Soda's (Egdworth) for the recorded monthly Cola sales for the three years 2003 to 2005, Le. from 1 January 2003 to 31December 2005. Montth sales of Cola (in hundreds of cases) 1400 1203' Monthly Sales 500 1000 500 200 Time Figure 1: Monthly cola sales \f