Question

I use 40 quarterly observations on a time series beginning with the first quarter of 2007 to estimate the following model: Y = 5 + 0.25 Trend + 1 Q2 – 2 Q3 + 0.5 Q4 Where Trend is a time index equal to 1 for the first observation and increases by 1 each quarter; Q2 is a dummy variable equal to 1 for all observations on the second quarter of a year and equal to 0 for all other observations; Q3 and Q4 are similarly defined. What are the forecasted values of Y for the four quarters of 2017? (time periods 41, 42, 43 and 44)?

24.25; 28.5; 25.75; 30.0

15.25; 16.5; 13.75; 16.5

5.25; 6.5; 3.75; 6.5

46.25; 48.25; 46.25; 49.75

Answer 1

Answer ---- 5.25; 6.5; 3.75; 6.5

For time period 41 - first quarter Q2=0, Q3=0,Q4=0

Trend =1

on substituting in : Y = 5 + 0.25 Trend + 1 Q2 – 2 Q3 + 0.5 Q4

we get Y = 5+ 0.25 =5.25

For time period 42 - second quarter Q2=1, Q3=0,Q4=0

Trend =2

on substituting in : Y = 5 + 0.25Trend + 1 Q2 – 2 Q3 + 0.5 Q4

we get Y = 5+ 0.5+ 1 =6.5

For time period 43 - third quarter Q2=0, Q3=1,Q4=0

Trend =3

on substituting in : Y = 5 + 0.25 Trend + 1 Q2 – 2 Q3 + 0.5 Q4

we get Y = 5+ 0.75 -2 = 3.75

For time period 44 - forth quarter Q2=0, Q3=0,Q4=1

Trend =4

on substituting in : Y = 5 + 0.25 Trend + 1 Q2 – 2 Q3 + 0.5 Q4

we get Y = 5+ 1 + 0.5 = 6.5