After fitting a Holt-Winters model on demand for a sport drink, we obtain the following values:

alpha = 0.436

gamma = 0.096

delta = 0.034

SSE = 188.475

s = 3.1103

sr = 0.1193

• Quarterly data is for eight years. We have obtained the following smoothed seasonality for the quarters in year 8.

Q1 sn_29 = 0.8044

Q2 sn_30 = 1.1538

Q3 sn_31 = 1.3434

Q4 sn_32 = 0.6908

• We have also obtained the following level and growth values for the latest quarter:

l₃₂ = 173.6213

b₃₂ = 3.0028

• Now assume we are in the beginning of year 9 and we observe the following demand in January (period 33):

y₃₃ = 129

Given this observation, answer the following questions.

Question 1

What is the estimated value of level in January of year 9 (l₃₃)?

173.0360

199.3504

172.3098

169.5364

Question 2

What is the estimated value of growth in January of year 9 (b₃₃)?

6.1734

2.3895

2.3224

1.9430

What is the new estimated value of seasonality for Q1 (sn_33)?

0.7064

0.8029

0.7456

0.6087

Question 4

What is the point forecast of demand in period 34 (Q2 year 9), given the observed demand in period 33, y₃₄ (33)?

138.243

278.238

210.640

198.291

What is the point forecast of demand in period 35 (Q3 year 9), given the observed demand in period 33, y₃₅ (33)?

140.111

233.995

230.875

229.047

question 6

What is the point forecast of demand in period 36 (Q4 year 9), given the observed demand in period 33, y₃₆ (33)?

121.929

159.880

118.720

141.979

Question 7

In order to estimate the 95% prediction interval of demand in period 34 (Q2 year 9), we need to compute ct=c1.

What is the value of c₁?

42240.04

29535.45

30617.64

30519.87

Question 8

What is the 95% prediction interval of demand in period 34 (Q2 year 9)?

You can assume that the point forecast of demand in this period y₃₄(33) = 200.09.

[185.54 , 200.13]

[167.77 , 232.42]

[-1008.73 , 1208.82]

[153.72 , 246.46]