Question

Consider the following time series.

Quarter	Year 1	Year 2	Year 3
1	71	68	62
2	48	40	50
3	59	61	54
4	78	81	72

(a) Construct a time series plot.

What type of pattern exists in the data?

a)The time series plot shows a horizontal pattern, but there is also a seasonal pattern in the data.

b)The time series plot shows a horizontal pattern with no seasonal pattern present.    

c)The time series plot shows a trend pattern, but there is also a seasonal pattern in the data.

d)The time series plot shows a trend pattern with no seasonal pattern present.

(b) Use the following dummy variables to develop an estimated regression equation to account for seasonal effects in the data:

x₁ = 1 if quarter 1, 0 otherwise; x₂ = 1 if quarter 2, 0 otherwise; x₃ = 1 if quarter 3, 0 otherwise.

= ______?________

(c)Compute the quarterly forecasts for next year.

quarter 1 forecast= ______?______

quarter 2 forecast=_____?________

quarter 3 forecast=_____?________

quarter 4 forecast=_____?_______

Answer 1

a)

a)The time series plot shows a horizontal pattern, but there is also a seasonal pattern in the data.

b)

Quarter	Period	Qtr1	Qtr2	Qtr3	Series
1	1	1	0	0	71
2	2	0	1	0	48
3	3	0	0	1	59
4	4	0	0	0	78
1	5	1	0	0	68
2	6	0	1	0	40
3	7	0	0	1	61
4	8	0	0	0	81
1	9	1	0	0	62
2	10	0	1	0	50
3	11	0	0	1	54
4	12	0	0	0	72

Applying multiple regression on above data:

y^ =81.5+(-10)X1+(-31)*X2+(-19)*X3

c)

forecast for 1st qtr of next year =			67
forecast for 2nd qtr of next year =			46
forecast for 3rd qtr of next year =			58
forecast for 4th qtr of next year =			77