Assume the following time series regression has been estimated for sales of gadgets: St = 20...

Assume the following time series regression has been estimated for sales of gadgets:

St = 20 + 13Q1 + 9Q2 +4Q3 + 2t + 3t2;

where t is the time trend and Q1, Q2 and Q3 are dummy variables for quarters 1, 2 and 3

respectively. Assume the data used in the regression starts in the first quarter of 2016 and ends

in the first quarter of 2018. Forecast the expected sales for quarters 2, 3 and 4 of 2018.

Solutions

Expert Solution

Assume the following time series regression has been estimated for sales of gadgets:

St = 20 + 13Q1 + 9Q2 +4Q3 + 2t + 3t2

where t is the time trend and Q1, Q2 and Q3 are dummy variables for quarters 1, 2 and 3

respectively. Assume the data used in the regression starts in the first quarter of 2016 and ends in the first quarter of 2018. Forecast the expected sales for quarters 2, 3 and 4 of 2018.

Understanding the dummy variable

Dummy variable for Q1, if the Quarter is 1, then Q1 = 1 or Q1 = 0

Dummy variable for Q2, if the Quarter is 2, then Q2 = 1 or Q2 = 0

Dummy variable for Q3, if the Quarter is 3, then Q3 = 1 or Q3 = 0

The trend (t) is shown below

Forecast for 2018 - Q2

Q1= 0
Q2 =1
Q3 = 0
t = 10

Regression equation

Forecast for 2018 - Q3

Q1= 0
Q2 =0
Q3 = 1
t = 11

Regression equation

Forecast for 2018 - Q3

Q1= 0
Q2 =0
Q3 = 0
t = 11

Regression equation

orchestra answered 1 year ago

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