Question 1. Consider the following time series data.
|
Week
|
1
|
2
|
3
|
4
|
5
|
6
|
|
Value
|
18
|
13
|
16
|
11
|
17
|
14
|
Using the naive method (most recent value) as the forecast for the next week, compute the following measures of forecast accuracy.
a. Mean absolute error.
b. Mean squared error.
c. Mean absolute percentage error.
d. What is the forecast for week 7?
Question 2. Ten weeks of data on the Commodity Futures Index are 7.35, 7.40, 7.55, 7.56, 7.60, 7.52, 7.52, 7.70, 7.62, and 7.55.
a. Construct a time series plot. What type of pattern exists in the data?
h. Compute the exponential smoothing forecasts for a = .2.
c. Compute the exponential smoothing forecasts for a = .3.
d. Which exponential smoothing constant provides more accurate forecasts based on MSE?
Question 3. Consider the following time series data.
t 1 2 3 4 5
Y 6 11 9 14 15
a. Construct a time series plot. What type of pattern exists in the data?
b. Develop the linear trend equation for this time series.
c. What is the forecast for t = 6?
Question 4. Consider the following time series data.
|
Quarter
|
Year 1
|
Year 2
|
Year 3
|
|
1
|
4
|
6
|
7
|
|
2
|
2
|
3
|
6
|
|
3
|
3
|
5
|
6
|
|
4
|
5
|
7
|
8
|
a. Construct a time series plot. What type of pattern exists in the data?
b. Use the following dummy variables to develop an estimated regression equation to account for any seasonal and linear trend effects in the data: Qtrl = 1 if Quarter 1, O. otherwise; Qtr2 = 1 if Quarter 2, 0 otherwise; Qtr3 = 1 if Quarter 3, 0 otherwise.
c. Compute the quarterly forecasts for next year.
Question 5. Consider the following time series data.
|
Quarter
|
Year 1
|
Year 2
|
Year 3
|
|
1
|
4
|
6
|
7
|
|
2
|
2
|
3
|
6
|
|
3
|
3
|
5
|
6
|
|
4
|
5
|
7
|
8
|
a. Construct a time series plot. What type of pattern exists in the data?
b. Show the four-quarter and centered moving average values for this time series.
c. Compute seasonal indexes and adjusted seasonal indexes for the four quarters.