Question

t 1 2 3 4 5

Yt 6 11 9 14 15

Refer to the time series above. Suppose the values of the time series for the next two time periods are 13 in period 6 and 10 in period 7. a. Construct a time series plot for the updated time series. What type of pattern exists in the data? b. develop the quadratic trend equation for the updated time series. c. use the quadratic trend equation developed in part (b) to compute the forecast for t 5 8. d. use the linear trend equation developed in exercise 17 to compute the forecast for t 5 8. Comment on the difference between the linear trend forecast and the quadratic trend forecast and what needs to be done as new time series data become available.

Answer 1

Given data:

t	Yt
1	6
2	11
3	9
4	14
5	15
6	13
7	10

a) Time series plot (drawn in excel) looks like:

b) The data shows non-linear pattern, so a polynomial curve looks fit for the data. Quadratic equation fitted to the data is shown above along with the quadratic equation.

c) The quadratic equation is: y = -0.5714x2 + 5.3571x + 1.1429

Hence, for t = 5, the forecast from quadratic trend equation is = -0.5714 * 5 + 5.3571 * 5 + 1.1429 = 13.64

And, for t = 8, the forecast from quadratic trend equation is = -0.5714 * 8 + 5.3571 * 8 + 1.1429 = 7.43

d) Linear trend equation is: y = 0.7857x + 8

Hence, for t=5, y = 11.93. And for t=8, y = 14.28

The linear trend forecast doesn't show the difference in forecast as properly as quadratic forecast, since the former doesn't model the scatter in data as closely as the quadratic forecast.

As new time series data becomes available, we need to re-calibrate the model to check if the earlier assumptions still hold true or not. This is because with time, the trend in data might have completely drifted from what it used to be initially.