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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)

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)

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)

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)

Grading

This assignment will be graded based on the following criteria: