ECON 2331: Economic and Business Statistics 2
Assignment 5, Part A (100 marks: 5%)
To receive full marks, you need to show all your work, including all the printouts.
1. The daily sales figures shown here have been recorded for Apple iPhone 6 in western Canada during the last month: (13 marks total)
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Weeks
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Day
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1
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2
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3
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4
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Monday
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38
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46
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35
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59
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Tuesday
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40
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36
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52
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53
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Wednesday
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17
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32
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25
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28
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Thursday
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20
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17
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28
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33
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Friday
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26
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20
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32
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20
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a. Compute the three-day and five-day moving averages; i.e., 3MA and 5MA. (4 marks)
b. Plot the series and the moving averages on the same graph. Does there
appear to be a seasonal (weekly) pattern? For this sales, would you prefer to use 3MA or 5MA? Why? (6 marks)
c. Calculate the five-day centered moving averages (3 marks)
2. The values of Alabama building contracts (in $ millions) for a 12-month period follow: (19 marks total)
240 350 230 260 280 320 220 310 240 310 240 230
a. Construct a time series plot. What type of pattern exists in the data? (4 marks)
b. Compare the three-month moving average approach with the exponential smoothing forecast using α=0.4. Which approach provides more accurate forecasts based on MSE? (6 marks)
c. What is the forecast for the next month? (3 marks)
d. Explain how you would find the optimum level of α for this data. (6 marks)
3. Air pollution control specialists in southern California monitor the amount of ozone, carbon dioxide, and nitrogen dioxide in the air on an hourly basis. The hourly time series data exhibit seasonality, with the levels of pollutants showing patterns that vary over the hours in the day. On July 15, 16, and 17, the following levels of nitrogen dioxide were observed for the 12 hours from 6:00 A.M. to 6:00 P.M. (14 marks total)
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July 15:
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25
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28
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35
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50
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60
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60
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40
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35
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30
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25
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25
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20
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July 16:
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28
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30
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35
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48
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60
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65
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50
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40
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35
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25
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20
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20
|
|
July 17:
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35
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42
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45
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70
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72
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75
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60
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45
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40
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25
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25
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25
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a. Construct a time series plot. What type of pattern exists in the data? (4 marks)
b. Use the following dummy variables to develop an estimated regression equation to account for the seasonal effects in the data. (10 marks)
Hour1=1 if the reading was made between 6:00 A.M. and 7:00 A.M.; Zero otherwise.
Hour2=1 if the reading was made between 7:00 A.M. and 8:00 A.M.; Zero otherwise.
Hour11=1 if the reading was made between 4:00 P.M. and 5:00 P.M.; Zero otherwise.
Note: that when the values of the 11 dummy variables are equal to zero, the observation corresponds to the 5:00 P.M. to 6:00 P.M. Hour.
c. Using the estimated regression equation developed in part (a), compute estimates of the levels of nitrogen dioxide for July 18. (4 marks)
d. Let t=1 to refer to the observation in hour 1 on July 15; t=2 to refer to the observation in hour 2 of July 15; … and t=36 to refer to the observation in hour 12 of July 17. Using the dummy variables defined in part (b) and in t, develop an estimated regression equation to account for seasonal effects and any linear trend in the time series. Based upon the seasonal effects in the data and linear trend, compute estimates of the levels of nitrogen dioxide for July 18. (14 marks)
4. The quarterly sales data (number of copies sold) for a college textbook over the past three years follow: (36 marks total)
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Year
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Quarter
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Sales
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1
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1
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1690
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2
|
940
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3
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2625
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4
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2500
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2
|
1
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1800
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2
|
900
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3
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2900
|
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4
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2360
|
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3
|
1
|
1850
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2
|
1100
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3
|
2930
|
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4
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2615
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a. Construct a time series plot. What type of pattern exists in the data? (4 marks)
b. Show the four-quarter and centered moving average values for this time series. (5 marks)
c. Compute the seasonal and adjusted seasonal indexes for the four quarters. (5 marks)
d. When does the publisher have the largest seasonal index? Does this result appear reasonable? Explain. (6 marks)
e. Deseasonalize the time series. (4 marks)
f. Compute the linear trend equation for the deseasonalized data and forecast sales, using the linear trend equation. (8 marks)
g. Adjust the linear trend forecasts, using the adjusted seasonal indexes computed in part (c). (4 marks)
Assignment 5, Part B (100 marks; 10%)
To receive full marks, you need to show all your work, including all the printouts.
The aim of Assignment 5, Part B is to explain the statistical techniques, tools, and methods covered in this course by applying them in real-world examples.
You must apply at least one of the techniques/methods learned in this course to real- world data in at least one area of Business and Economics. The data for such a case could either be primary or secondary. The expected length of this assignment is 1,000 words. A scan of all your data, outputs, and findings from your software (e.g., Excel®, or XLSTAT®) must be included in the appendix of the assignment (and is not included in the word count).
Topics
Topics for this assignment are to be proposed by you and approved by your Open Learning Faculty Member. You may start with the Case Problems provided at the end of chapters of the textbook and extend the techniques or update the data of the Case Problems to real-world data. Alternatively, you may apply the techniques covered in this course to your choice of real-world data. In either case, the topic and the methods you select for this assignment must first be approved by your Open Learning Faculty Member.
Data
You may obtain the required data from the industry/place you work, or would like to work.
You can also obtain the data from Thompson Rivers University Library. See the Course Guide for more about the library or visit the library’sDROL website at http://www.tru.ca/library/services/distance.html.
Grading
This assignment will be graded based on the following criteria:
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Criteria for Assignment
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Available Mark
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Mark Given
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Relevant and clear title with a title
page, student name, student number and a short biography. The document is typed, double spaced and looks
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5
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Abstract: 250 words (not included in the 1,000 word count for the main
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10
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Introduction
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5
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Objective(s)
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8
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Methodology
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15
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Empirical Results
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25
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Conclusions
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7
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Discussions
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5
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Future Research
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5
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References (minimum 3 references)
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10
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Appendices (all software printouts are included)
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5
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100
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