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Time Series Forecasting Models

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Please help with the following questions.

Question 1
Determine the error for each of the following forecasts. Then, calculate MAD and MSE.

Period Value Forecast Error
1 202 — —
2 191 202
3 173 192
4 169 181
5 171 174
6 175 172
7 182 174
8 196 179
9 204 189
10 219 198
11 227 211

Question 2
The U.S. Census Bureau publishes data on factory orders for all manufacturing, durable goods, and nondurable goods industries. Shown here are factory orders in the United States over a 13-year period ($ billion).
First, use these data to develop forecasts for the years 6 through 13 using a 5-year moving average.

Then, use these data to develop forecasts for the years 6 through 13 using a 5-year weighted moving average. Weight the most recent year by 6, the previous year by 4, the year before that by 2, and the other years by 1.
Answer the following questions:

a) What is the forecast for year 13 based on the 5-year moving average?
b) What is the forecast for year 13 based on the 5-year weighted moving average?
c) What is the MAD for the moving average forecast?
d) What is the MAD for the weighted moving average forecast?
e) Which forecasting model is better?

Year Factory Orders
($ billion)
1 2,512.70
2 2,739.20
3 2,874.90
4 2,934.10
5 2,865.70
6 2,978.50
7 3,092.40
8 3,111.10
9 3,222.20
10 3,555.00
11 4,221.50
12 4,551.20
13 4,137.00

Question 3
The "Economic Report to the President of the United States" included data on the amounts of manufacturers' new and unfilled orders in millions of dollars. Shown here are the figures for new orders over a 21-year period.
Use the Charting tool in Excel to develop a regression model to fit the trend effects for these data. Use a linear model and then try a polynomial (order 2) model. Make sure the charts show the line formula and the r-squared value. Include both charts in your report. Then answer the following question:
• How well does either model fit the data? Which model should be used for forecasting? Explain using the relevant metrics.

Year Total Number of New Orders
1 55,022
2 55,921
3 64,182
4 76,003
5 87,327
6 85,139
7 99,513
8 115,109
9 116,251
10 121,547
11 123,321
12 141,200
13 162,140
14 168,420
15 171,250
16 176,355
17 195,204
18 209,389
19 237,025
20 272,544
21 293,475

Template for answers:

In the summary tables below, insert only the answers. You will show work after the summary section.

Question 1
MAD
MSE

Question 2
a) Moving average forecast for year 13
b) Weighted moving average forecast for year 13
c) MAD for part a
d) MAD for part b
e) Recommended forecast method (justify):

Question 3
R-squared for Linear model
R-squared for polynomial model
Regression formula for linear model
Regression formula for polynomial model
Recommended forecast method (justify):

Work
Show all your work for the questions below.
Question 1
Show the errors you calculated.
Question 2
Show the two forecasts and the errors.
Question 3
Show the regression output tables.

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Solution Summary

The solution provides step by step method for the calculation of trend for time series models. Formula for the calculation and interpretations of the results are also included.

Solution Preview

Please see the attachments for full solutions and steps.

Question 1
MAD 12.5
MSE 191.9

Question 2
a) Moving average forecast for year 13 $3732.2 billion
b) Weighted moving average forecast for year 13 $4116.89 billion
c) MAD for part a ...

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