Question

The following table shows the quarterly demand in thousands of cases, for a national beer distributor over the past four years. This data is also available in an Excel spreadsheet on Blackboard.

	Year
Quarter	2015	2016	2017	2018
1	280	321	419	266
2	485	493	502	510
3	423	515	487	501
4	330	271	468	516

Forecast the demand for each quarter of 2019 by using the multiplicative decomposition model and using overall average to calculate seasonal indices.. Show:

- the MAD and MAPE

- a plot of the actuals and seasonalized forecast on a properly labeled chart.

- the forecast for each quarter of 2019

Answer 1

Multiplicative models:

In many time series involving quantities (e.g. money, wheat production, ...), the absolute differences in the values are of less interest and importance than the percentage changes.

For example, in seasonal data, it might be more useful to model that the July value is the same proportion higher than the January value in each year, rather than assuming that their difference is constant. Assuming that the seasonal and other effects act proportionally on the series is equivalent to a multiplicative model,

Fortunately, multiplicative models are equally easy to fit to data as additive models! The trick to fitting a multiplicative model is to take logarithms of both sides of the model,

seasonal index:

A season index is defined by: