Case Assignment 1 – 06/02/2020
(Questions 3.1, 3.3, 3.4, 3.7, 3.8 – source: “Principles of Business Forecasting” 2nd edition; Ord, Fildes, Kourentzes)
Question 4:
Sales for air conditioning units (in ‘000) over the last 8 years are recorded on a quarterly basis (see data “AC”). A time plot of the time series suggests that the sales trend increases linearly, and that the seasonal pattern increases as the level of the series increases (ie: increasing seasonal variation). These combined patterns call for a Holt-Winters’ method with multiplicative seasonality,
a – Use the first 2 years of data to determine the starting values for series components: level, trend, and seasonal. What are these values?
b – Find optimal smoothing constants for each time series component, using the data for Year1 – Year4 (inclusive) as the training sample. You may use the ESM macro or another suitable software to complete this exercise.
c- Identify the final estimates for level and trend for the last quarter of Year8, and the final estimates for the four seasonal factors in Year8.
d – Compute point forecasts and 95% prediction intervals for all quarters of the next year, Year9. Assume that error terms are normally distributed here.