# Time Series Forecasting Models

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.

https://brainmass.com/statistics/sampling-distribution/time-series-forecasting-models-592651

#### 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 ...

#### 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.