Question

Consider the following time series data (Insert the data in an Excel file):

v

QUARTER	YEAR 1	YEAR2	YEAR 3	YEAR 4
1	8	9	12
2	5	6	9
3	7	8	10
4	8	11	11

2.1. Construct a time series plot. What type of pattern exists in the data?

2.2. Use a multiple regression model with dummy variables as follows to develop an equation to account for seasonal effects in the data. Qtr1=1 if quarter 1, 0 otherwise; Qtr2=1 if quarter 2, 0 otherwise; Qtr3=1 if quarter 3, 0 otherwise.

2.3. Use a multiple regression model to develop an equation to account for trend and seasonal effects in the data. Use the dummy variables you developed in part 2.2 to capture seasonal effects and create a variable t such that t =1 for quarter 1 in year 1, t =2 for quarter 2 in year 1, . . . t =12 for quarter 4 in year 3.

2.4. Calculate MSE for both models. Which model (2.2 or 2.3) is more accurate? Why?

2.5. Forecast the time series for Year 4, Quarters 1, 2, 3, 4.

Answer 1

1. The time series plot is:

Horizontal pattern with seasonality

2. y = 10 - 0.333*Qtr 1 - 3.333*Qtr 2 - 1.667*Qtr 3

3. y = 6.5 + 0.979*Qtr 1 - 2.458*Qtr 2 - 1.229*Qtr 3 + 0.438*t

4.

	2.2	2.3
MSE	3.5000	0.5000

2.3 is more accurate because it has a lower MSE value.

5.

Forecast

13.167

10.167

11.833

13.5