For Part 1 and 2, using the following demand data over two years and a total of eight quarters.

Period t	Year, Quarter	Demand Dt	Level Lt	Trend Tt	Forecast Ft
0			Assume L0=220
1	Year 1, Q1	225
2	Year 1, Q2	174
3	Year 1, Q3	241
4	Year 1, Q4	727
5	Year 2, Q1
6	Year 2, Q2
7	Year 2, Q3
8	Year 2, Q3

Part 1: Simple Exponential Smoothing ( = 0.4)

1. Estimate level component (L_t) for periods 1-4.
2. Forecast demand (F_t) for periods 1-4.
3. Forecast demand (F_t) for periods 5-8.

Part 2: Holts model ( = 0.4, = 0.2)

Obtain the initial level L0 and trend T0 using the regression approach discussed in the text.

1. Period 1: Estimate level component (L1) and trend component (T1).
2. Period 2: Estimate level component (L2) and trend component (T2).
3. Period 3: Estimate level component (L3) and trend component (T3).
4. Period 4: Estimate level component (L4) and trend component (T4).
5. Forecast demand (Ft) for periods 1-4.
6. Forecast demand (Ft) for periods 5-8.

Part 3: Winters Model

Now, assume the following is the demand for the past 4 years:

Year	Quarter	Period	Demand	Level	Trend	Seasonal factors
		0		L0 = ?	T0 = ?
1	I	1	225			S1 = ?
	II	2	174			S2 = ?
	III	3	241			S3 = ?
	IV	4	727			S4 = ?
2	I	5	351
	II	6	214
	III	7	346
	IV	8	706
3	I	9	412
	II	10	277
	III	11	255
	IV	12	825
4	I	13	549
	II	14	438
	III	15	431
	IV	16	1203
5	I	17	?
	II	18	?
	III	19	?
	IV	20	?

Use the winters method with = 0.4, = 0.2, = 0.1

Obtain the initial level and trend estimates using the regression method.

Obtain the initial seasonal factors using the static method.

Forecast the demand for Year 5 (Period 17-20).

Calculate forecast errors: MSE, MAD, and TS.

Hint: Similar to the Tahoe Salt example.

First, obtain the initial level (L₀) and trend (T₀) estimates and the initial seasonal factors (S1-S4) using the static method (p.182-p.187).

Second, update level, trend, and seasonal factors using Eq. 7.18, 7.19, 7.20.

Third, forecast the demand for Year 5 (Period 17-20) using Eq. 7.17.

PART 4:

Which forecasting method is the best? Why?