Question

Consider the following time series.

Quarter	Year 1	Year 2	Year 3
1	71	68	62
2	50	42	52
3	59	61	54
4	78	81	72

(a)

Construct a time series plot.

  

What type of pattern exists in the data?

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

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

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

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)

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

b)

Applying multiple regression on above data from excel: data-data analysis: regression:

y^ =77-10x1-29x2-19x3

c)

forecast for 1st qtr of next year =			67
forecast for 2nd qtr of next year =			48
forecast for 3rd qtr of next year =			58
forecast for 4th qtr of next year =			77