Consider the following time series data. (a) Construct a time series plot. ® 30 25+ 20- 15- 10- 5 1 Month 12 3 4 5 Value 24 13 20 12 19 Month 2 3 4 5 0- C 1 2 3 What type of pattern exists in the data? The data appear to follow a horizontal pattern. O The data appear to follow a seasonal pattern. O The data appear to follow a trend pattern. O The data appear to follow a cyclical pattern. 6 7 30 T 30 25- 25 20- 20 15- mimi ww 15- 10- 10 5 0 0 1 2 3 4 5 6 Month (b) Develop the three-month moving average forecasts for this time series. Time Series Value Compute MSE. MSE=18.09 24 13 20 12 4 Month 19 23 15 19 5 17.25 17.6 Forecast 6 18.50 x What is the forecast for month 8? 126 |x 23 15 6 ]✓ x 7 x x 7 8 0 1 2 3 4 5 Month 6 7 8 ⓇO 30 23 20- 15 10- 5 0 0 1 2 3 4 5 Month 7 8 O 7 8 Ⓡ
Consider the following time series data. (a) Construct a time series plot. ® 30 25+ 20- 15- 10- 5 1 Month 12 3 4 5 Value 24 13 20 12 19 Month 2 3 4 5 0- C 1 2 3 What type of pattern exists in the data? The data appear to follow a horizontal pattern. O The data appear to follow a seasonal pattern. O The data appear to follow a trend pattern. O The data appear to follow a cyclical pattern. 6 7 30 T 30 25- 25 20- 20 15- mimi ww 15- 10- 10 5 0 0 1 2 3 4 5 6 Month (b) Develop the three-month moving average forecasts for this time series. Time Series Value Compute MSE. MSE=18.09 24 13 20 12 4 Month 19 23 15 19 5 17.25 17.6 Forecast 6 18.50 x What is the forecast for month 8? 126 |x 23 15 6 ]✓ x 7 x x 7 8 0 1 2 3 4 5 Month 6 7 8 ⓇO 30 23 20- 15 10- 5 0 0 1 2 3 4 5 Month 7 8 O 7 8 Ⓡ
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
Transcribed Image Text:Consider the following time series data.
Month 1 2 3
Value 24 13 20
(a) Construct a time series plot.
30
25-
1
20
15
2
Month
4
What type of pattern exists in the data?
The data appear to follow a horizontal pattern.
O The data appear to follow a seasonal pattern.
3
5
O The data appear to follow a trend pattern.
O The data appear to follow a cyclical pattern.
5
7
6
6
(b) Develop the three-month moving average forecasts for this time series.
Time Series
Value
30
25
25
20
20-
15
mimi ww
15-
10+
10-
5
0
0 1 2 3 4 5 6 7 8
Month
Compute MSE.
MSE 18.09
24
13
20
12
19
23
15
5
19
17.25
17.6
12 19 23 15
Forecast
18.50
6
1x
What is the forecast for month 8?
126
x
7
x
x
x
30
0
0 1 2
3 4 5
Month
7
8
30
25
20-
15
10
5
0 1
2
3 4 5
Month
6
7
8
O
O✓
0
0
1
3 4
Month
5 6
+
7
8
0
Transcribed Image Text:(c) Use a = 0.2 to compute the exponential smoothing forecasts for the time series. (Round your answers to two decimal places.)
Time Series
Value
Month
1
2
لیا
4
5
6
7
Month
1
2
24
3
13.
4
20
5
12
6
19
Compute MSE. (Round your answer to two decimal places.)
MSE=
What is the forecast for month 8? (Round your answer to two decimal places.)
23
(d) Compare the three-month moving average approach with the exponential smoothing approach using a = 0.2. Which appears to provide more accurate forecasts based on MSE?
O The exponential smoothing using a = 0.2 provides a better forecast since it has a larger MSE than the three-month moving average.
O The exponential smoothing using a = 0.2 provides a better forecast since it has a smaller MSE than the three-month moving average.
15
The three-month moving average provides a better forecast since it has a smaller MSE than the exponential smoothing using a = 0.2.
O The three-month moving average provides a better forecast since it has a larger MSE than the exponential smoothing using a = 0.2.
(e) Use a smoothing constant of a = 0.4 to compute the exponential smoothing forecasts. (Round your answers to two decimal places.)
Time Series
Value
24
13.
20
24
12
17.6
19
23
15
Forecast
24
19
x
18.50
Forecast
17.6
17.25
x
X
X
Does a smoothing constant of 0.2 or 0.4 appear to provide more accurate forecasts based on MSE? Explain.
O The exponential smoothing using a = 0.2 provides a better forecast since it has a smaller MSE than the exponential smoothing using a = 0.4.
The exponential smoothing using a = 0.4 provides a better forecast since it has a smaller MSE than the exponential smoothing using α = 0.2.
O The exponential smoothing using a = 0.4 provides a better forecast since it has a larger MSE than the exponential smoothing using α = 0.2.
O The exponential smoothing using a = 0.2 provides a better forecast since it has a larger MSE than the exponential smoothing using a = 0.4.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 6 steps with 11 images
Recommended textbooks for you
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman