Suppose the following are the seasonal indices for the first

Suppose the following are the seasonal indices for the first three quarters of the year for a quarterly series: Quarter Seasonal Index

Q1 73.9

Q2 84.1

Q3 107.1

Remember that the seasonal indices should average 100 so you should be able to infer the seasonal index for Q4.

Furthermore, suppose that the estimated coeffcients from a regression of the deseasonalized series on Time are given below:

Coefficients Intercept 2,964

Time 50.7

What is the trend projection of the series for period 119?

Solution

When we fit mathematical trend equation to a time series then we assume a linear equation of the form T(t) = a + bt where T(t) is the time series trend component value and t is the time period. a and b are the unknown parameter coeffecients. To fit this equation we first deseasonalise the data by subtracting the seasonal components from the actual time series values and then use method of least squares ti estimate a and b. However here values of a nd b has been provided respectively as 2964 and 50.7.also there is no need to find the 4th seasonal component as we are to find the trend component only. so simply put t=119 in T(t) = 2964+(50.7*119) and get the trend component = 8997.3 which is the answer.