Question

Consider the following time series data.

Quarter	Year 1	Year 2	Year 3
1	2	4	5
2	4	5	8
3	1	3	4
4	7	9	10

(a)

Choose the correct time series plot.

(i)
(ii)
(iii)
(iv)

- Select your answer -Plot (i)Plot (ii)Plot (iii)Plot (iv)Item 1

What type of pattern exists in the data?

- Select your answer -Positive trend pattern, no seasonalityHorizontal pattern, no seasonalityNegative trend pattern, no seasonalityPositive trend pattern, with seasonalityHorizontal pattern, with seasonalityItem 2

(b)

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.

If required, round your answers to three decimal places. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank. (Example: -300) If the constant is "1" it must be entered in the box. Do not round intermediate calculation.

ŷ =   +   Qtr₁ +   Qtr₂ +   Qtr₃

(c)

Compute the quarterly forecasts for next year based on the model you developed in part (b).

If required, round your answers to three decimal places. Do not round intermediate calculation.

Year	Quarter	Ft
4	1
4	2
4	3
4	4

(d)

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 (b) 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.

If required, round your answers to three decimal places. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank. (Example: -300)

ŷ =   +  Qtr₁ +  Qtr₂ +  Qtr₃ +   t

(e)

Compute the quarterly forecasts for next year based on the model you developed in part (d).

Do not round your interim computations and round your final answer to three decimal places.

Year	Quarter	Period	Ft
4	1	13
4	2	14
4	3	15
4	4	16

(f)

Is the model you developed in part (b) or the model you developed in part (d) more effective?

If required, round your intermediate calculations and final answer to three decimal places.

	Model developed in part (b)	Model developed in part (d)
MSE

- Select your answer -Model developed in part (b)Model developed in part (d)Item 22

Justify your answer.

Answer 1

(a) The correct time series plot is:

Horizontal pattern with seasonality

(b) ŷ = 8.667 - 5 Qtr1 - 3 Qtr2 - 6 Qtr3

(c)

Ft

3.667

5.667

2.667

8.667

(d) ŷ = 5.417 - 3.781 Qtr1 - 2.188 Qtr2 - 5.594 Qtr3 + 0.406 t

(e)

Ft

6.917

8.917

5.917

11.917

(f)

	Model developed in part (b)	Model developed in part (d)
MSE	2.833	0.220

The model developed in part (d) because it has a lower MSE.

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