1. Let yt, t = 1,...,T , a time series, characterized by a linear trend, no cyclical and seasonal variations. Prove that the linear regression method corresponds to the elementary technique when r = 2.
2. Euro Pack is a leading European firm of packaging products. The plant located in Denmark realizes, in a continuous cycle, more than 150 products in 60 g/m2 polyethylene and nylon film.
(a) Estimate the amount of polyethylene and nylon film needed to ensure daily production in the next week by using historical data related to the last 30 days (shown in Table).
(b) Determine the tracking signal (band ±4) at the current time period.
(c) Determine the interval forecast of polyethylene and nylon films for one day ahead with respect to T = 30, with a level of confidence (1 - α) = 0.95.
