Statistics- Person 1 assumes a multiplicative seasonal model

| March 30, 2017

Question
Homework 3: February 10 (Due on February 17, Wednesday)
Two people make independent forecasts of quarterly sales with seasonal effects.
• Person 1 assumes a multiplicative seasonal model, and uses exponential
smoothing to forecast yearly sales and simple averaging to forecast season
effects (in %). The initial guess is that yearly sales is 5 units, distributed
uniformly over 4 quarters (25% per quarter). The value of α is set at 0.5
to update forecasts.
• Person 2 assumes an additive seasonal model, and uses exponential smoothing to forecast both average quarterly sales and quarterly deviations. The
value of α is 0.5 in all cases. As the initial guess, the average quarterly
sales is 2 units and deviation is 0 in each quarter.
The observed quarterly sales data in the first 6 years is as follows
year
year
year
year
year
year

1
2
3
4
5
6

1.40
2.12
2.62
3.17
4.14
4.49

3.13
3.80
5.25
6.58
7.89
8.87

3.90
4.58
6.45
7.85
9.26
10.59

2.17
2.74
3.65
4.47
5.37
6.07

Questions:
1. demonstrate how each of the two forecast procedures plays out in these
six years.
2. calculate the sum of squared residues (SSR) of the four quarterly sales
forecasts in year 6 to determine which model is better.

1

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