TIME SERISE ANALYSIS AND FORECASTING (SMOOTHING METHODS)
Part I Select the correct answer and write the appropriate letter in the space provided.
1. A listing of values over a period of time is called a
a. trend.
b. time series.
c. seasonal index.
d. residual.
2. The long-term behavior of a variable over an extended period of time is called
a. the seasonal index.
b. the cyclical variation.
c. the trend.
d. episodic variation.
3. A period of prosperity followed by recession is called the
a. cyclical variation.
b. trend.
c. seasonal variation.
d. irregular variation.
4. When we plot a trend equation, the variable plotted along the horizontal axis is
a. the dependent variables.
b. sales.
c. time.
d. log of time.
5. The variation within a year, such as retail sales during the Christmas holidays, is called the
a. trend.
b. seasonal variation.
c. irregular variation.
d. cyclical variation.
6. In June the Youngsville TrueValue Hardware store suffered severe damage to its contents during a flood. This is an example of
a. residual variation.
b. cyclical variation.
c. episodic variation.
d. seasonal variation because it happened during the summer.
7. The purpose of determining the ratio-to-moving average when computing a seasonal index is to eliminate the
a. random variation.
b. trend.
c. cyclical variation.
d. all of the above.
8. The reason for centering a moving average is to
a. convert the average to an index.
b. remove the random variation.
c. find the correction factor.
d. align the time periods.
9. A monthly index is being developed for the company sales. The moving total will consist of
a. four quarterly sales values.
b. logs of sales.
c. logs of quarters.
d. twelve monthly sales values.
10. The index for October for imports by Wines, Inc. is 90. The actual imports for October were $450,000. The seasonally adjusted imports are
a. $405,000.
b. $450,000.
c. $500,000.
d. none of the above.
11. Forecasting time horizons include:
a. Long range.
b. Medium range.
c. Short range.
d. all of the above.
12. Qualitative methods of forecasting include:
a. Sales forecast composite.
b. Jury of executive opinions.
c. Customer market survey.
d. all of the above.
13. Three popular measures of forecast accuracy are:
a. Total error, average error, and mean error.
b. Average error, median error, maximum error.
c. Median error, minimum error, and maximum absolute error.
d. Mean Absolute deviation, mean squared error, and mean absolute percent error.
14. Average demand for iPods in the Rome, Italy, Apple store is 800 units per month.
The May monthly index is 1.25. What is the seasonally adjusted sales forecast for May?
a. 640 units.
b. 798.75 units.
c. 800 units.
d. 1000 units.
15. The tracking signal is the:
a. standard error of the estimate.
b. Ratio of the cumulative error to MAD.
c. Mean Absolute deviation (MAD).
d. Mean absolute percent error.
16. The difference between a moving average model and exponential smoothing model is that:
17. The main difference between simple and multiple regression is:
Part II Record the answers in the space provided. Show essential calculations.
18. Shown below are the net sales for the J. M. Smucker Company, a leading marketer of jams and jellies.
19. The following table shows the number of homes built by Custom Builders, Inc. in the last four years by quarter. Develop a seasonal index for each quarter using the ratio-to- moving average method.
20. Listed below is the number of movie tickets sold at Library Cinema Complex, in thousands, for the period from 1996 to 2008. Compute a five-year weighted moving average using weights of 0.1, 0.1, 0.2, 0.3, and 0.3, respectively. Describe the trend in yield.
21. Sally's Software, Inc., is a rapidly growing supplier of computer software to the Sarasota area. Sales for the last five years are given on the left.
1/ plot the sales data.
2/ Determine the logarithmic trend equation.
3/ By what percent did sales increase, on the average, during the period? 4/ Estimate sales for the year 2009?
22. Westberg Electric Company sells electric motors to customers in the Jamestown, New York, area. The monthly trend equation, based on five years of monthly data, is Y = 4.4 + 0.5t
The seasonal factor for the month of January is 120, and it is 95 for February. Determine the Seasonally adjusted forecast for January and February of the sixth year.
23. Refer to Exercise#9 on page: 537. The production manager of High Point Sofa Chair, a large furniture manufacturer located in North Carolina, is studying the job performance ratings of a sample of 15 electrical repairmen employed by the company.
An aptitude test is required by the human resources department to become an electrical repairman. The production manager was able to get the score for each repairman in the sample.
In addition, he determined which of the repairmen were union member (code =1) and which were not (code = 0). The sample information is reported below.
2/ Test for autocorrelation at the 0.05 significance level. H0: No residual correlation
H1: Positive residual correlation
24. Appliance Center sells a variety of electronic equipment and home appliances. For the last four years the following quarterly sales (in $ millions) were reported.
2/ Explain the typical indexes for each season. Total sales for the first quarter are typically Total sales for the second quarter are typically Total sales for the third quarter are typically Total sales for the fourth quarter are typically
25. The planning department of Padget and Kure Shores, the manufacturer of an exclusive brand of women's shores, developed the following trend equation, in millions of pairs based on five years of quarterly data. Y = 3.30 + 1.75t
26.
1/ plot the data on a graph. Do you observe any trend, cycles, or random variations?
2/ Starting in year 4 and going to year 12, forecast demand using a 3-year moving average. Plot your forecast on the same graph as the original data.
3/ Starting in 4 and going to year 1, forecast demand using a 3-year moving average with weights of 0.1, 0.3, and 0.6, using 0.6 for the most recent year. Plot this forecast on the same graph.
4/ As you compare forecasts with the original data, which seems to give the better results? The 3-years moving average.
27.Develop a forecast for years 2 through 12 using exponential smoothing with α = 0.4 and a forecast for year 1 of 6. Plot your new forecast on a graph with the actual values and the naïve forecast. Based on a visual inception, which forecast is better?
28. Emergency calls to the 911 system of Durham, North Carolina, for the past 24 weeks are shown in the following table:
Forecast calls for weeks 2 through 25 with a trend-adjusted exponential smoothing model. Assume an initial forecast for 50 calls for week 1 and an initial trend of zero. Use smoothing constant α = 0.3 and β = 0.2.
29. Lenovo uses the ZX-81 chip in some of its laptop computers. The price for the chip during the past 12 months were as follow:
1/ Use a 2-month moving average on all the data and plot the averages and the prices.
2/ Use a 3-month moving average and add the 3-month plot to the graph created in part(1)
3/ Which is better (using the mean absolute deviation): the 2-month average or the 3 -month average?
4/ Compute the forecast for each month using exponential smoothing, with an initial forecast for January of $1.80. Use α = 0.1, then α = 0.3, and finally α = 0.5. Using MAD which α is the best?
30. Following are two weekly forecasts made by two different methods for the number of gallons of gasoline, in thousands, demanded at a local gasoline station. Also, shown are actual demand levels, in thousands of gallons.
31. The number of internal disk drives (in millions) made at a plant in Taiwan during the past 5 years follows:
1/ Forecast the number of disk drives to be made next year, using linear regression. 2/ Compute the mean squared error (MSE) when using linear regression.
32. The following are monthly actual and forecast demand levels for May through December for units of a product manufactured by the D. Bishop Company in Des Moines:What is the value of the tracking signal as of the end of December?
Attachment:- case.rar