Questions and Answers of Forecasting Predictive Analytics

4.8 Using the data in Table 4-7, use Pegels' cell C-3 to model the data. First, examine the equations that go along with this method (see Table 4-10), then pick speci¯c values for the three
4.7 Forecast the airline passenger series given in Table 3-5 two years in advance using whichever of the following methods seems most appropriate: single exponential forecasting, Holt's method,
4.6 Using the data in Table 4-5, examine the in°uence of di®erent starting values for ® and di®erent values for ¯ on the ¯nal value for ® in period 12. Try using ® = 0:1 and ® = 0:3 in
(e) Study the autocorrelation functions for the forecast er-rors resulting from the two methods applied to the two data series. Is there any noticeable pattern left in the data?
(d) Compare the forecasts for the two methods and discuss their relative merits.
(c) Compare the error statistics and discuss the merits of the two forecasting methods for these data sets.
(b) Repeat using the method of linear exponential smoothing(Holt's method).
(a) Use single exponential smoothing and compute the mea-sures of forecasting accuracy over the test periods 11{30.
4.5 The data in the following table show the daily sales of pa-perback books and hardcover books at the same store. The task is to forecast the next four days' sales for paperbacks and hardcover
(d) How do these two moving average forecasts compare?
(c) Now compute a new series of moving average forecasts using six observations in each average. Compute the errors as well.
(b) Compute the error in each forecast. How accurate would you say these forecasts are?
(a) Compute a forecast using the method of moving averages with 12 observations in each average.
Using the monthly data given below:
4.4 The Paris Chamber of Commerce and Industry has been asked by several of its members to prepare a forecast of the French index of industrial production for its monthly newsletter.
(c) What values of ® and ¯ did you use in (ii) above? Why?
(b) What value of ® did you use in (i) above? How can you explain it in light of equation (4.4)?
(a) Which of the two methods is more appropriate? Why?
Find the optimal parameters in both cases.
(ii) Holt's method of linear exponential smoothing.
4.3 Using the single randomless series 2, 4, 6, 8, 10, 12, 14, 16, 18, and 20, compute a forecast for period 11 using:
(c) Assuming that the past pattern will continue into the future, what k and ® values should management select in order to minimize the errors?
(b) What will the forecasts be for May 1992 for exponential smoothing with ® values of 0.1, 0.3, 0.5, 0.7, and 0.9?
wants to use both moving averages and expo-nential smoothing as methods for forecasting sales. Answer the following questions:(a) What will the forecasts be for May 1992 using a 3-, 5-, 7-, 9-, and
4.2 The following data re°ect the sales of electric knives for the period January 1991 through April 1992:1991 1992 Jan 19 Jan 82 Feb 15 Feb 17 Mar 39 Mar 26 Apr 102 Apr 29 May 90 Jun 29 Jul 90 Aug
(c) Compare your two estimates using the accuracy statis-tics.
(b) Repeat using single exponential smoothing with ® = 0:7.
(a) Estimate unemployment in the fourth quarter of 1975 using a single moving average with k = 3.
4.1 The Canadian unemployment rate as a percentage of the civilian labor force (seasonally adjusted) between 1974 and the third quarter of 1975 is shown below.Quarter Unemployment Rate 1974 1 5.4 2
Theil's U-statistic (a compromise between absolute and relative Theil's U measures) is very useful. In row 1, U = 1:81, indicating a poor¯t, far worse than the aÄ³ve model," which would simply use
² The lag 1 autocorrelation (r1) is a pattern indicator|it refers lag 1 ACF to the pattern of the errors. If the pattern is random, r1 will be around 0. If there are runs of positive errors
The minimum MSE (mean square error) is obtained for Pegels' optimal model cell B-3 method (row 8) when optimum values for the three parameters are determined. The same model also gives the minimum
The MAPE (mean absolute percentage error) is another use- MAPE ful indicator but gives relative information as opposed to the absolute information in MAE or MSE.
Forecasts from single exponential smoothing and Holt's method for quarterly sales data. Neither method is appropriate for these data
(c) Is the recession of 1991/1992 visible in the estimated components?
(b) Write about 3{5 sentences describing the results of the seasonal adjustment. Pay particular attention to the scales of the graphs in making your interpretation.
(a) Say which quantities are plotted in each graph.
3.8 Figure 3-13 shows the result of applying STL to the number of persons in the civilian labor force in Australia each month from February 1978 to August 1995.
(c) Comment on these results and their implications for forecasting.
Use a classical multiplicative decomposition to estimate the seasonal indices and the trend.
3.5 The data in Table 3-11 represent the monthly sales of product A for a plastics manufacturer for years 1 through 5.1 2 3 4 5 Jan 742 741 896 951 1030 Feb 697 700 793 861 1032 Mar 776 774 885 938
(c) Explain how you handled the end points.
(b) Using an classical additive decomposition, calculate the seasonal component.
(a) Estimate the trend using a centered moving average.
3.4 Consider the quarterly electricity production for years 1{4:Year 1 2 3 4 Q1 99 120 139 160 Q2 88 108 127 148 Q3 93 111 131 150 Q4 111 130 152 170
(b) Write the whole smoothing operation as a single weighted moving average by ¯nding the appropriate weights.
(a) Explain the choice of the smoother lengths in about two sentences.
3.2 Show that a 3 £ 5 MA is equivalent to a 7-term weighted moving average with weights of 0.067, 0.133, 0.200, 0.200, 0.200, 0.133, and 0.067.3.3 For quarterly data, an early step in seasonal
Period Shipments Period Shipments 1 42 9 180 2 69 10 204 3 100 11 228 4 115 12 247 5 132 13 291 6 141 14 337 7 154 15 391 8 171
3.1 The following values represent a cubic trend pattern mixed with some randomness. Apply a single 3-period moving average, a single 5-period moving average, a single 7-period moving average, a
the seasonal component can be forced to be constant over time(i.e., the same seasonal component for each year);holiday e®ects ² holiday factors (such as Easter, Labor Day, and Thanksgiving)be
Other changes in the level of the series such as level shifts and temporary ramp e®ects can also be modeled.missing values in the series can be estimated and replaced;
Outliers arise because of unusual circumstances such as major strikes. These e®ects can also be removed prior to decomposi-tion.
A seasonal sub-series plot for the decomposition shown in Figure 3-11. The seasonal component for June, July, and August became larger over the period of the data, with corresponding falls in
(g) The world motor vehicle market was greatly a®ected by the oil crisis in 1973{1974. How did it a®ect Japanese motor vehicle production? If this information could be included in the forecasts,
(f) From the graphs you have made, can you suggest a better forecasting method?
(e) Transform your forecast for 1990 back to the original scale by ¯nd the exponential of your forecast in (c). Add the forecast to your graph.
(d) Compute the forecast errors and calculate the MSE and MAPE from these errors.
(c) Calculate forecasts for the transformed data for each year from 1948 to 1990 using NaÄ³ve Forecast 1.
(b) Transform the data using logarithms and do another time plot.
(a) Plot the data in a time plot. What features of the data indicate a transformation may be appropriate?
2.8 Japanese motor vehicle production for 1947{1989 is given in Table 2-22.
(e) Show that the graphed forecasts are identical to extend-ing the line drawn between the ¯rst and last observations.
(d) Add the forecasts to the graph.
(c) From these forecasts, compute forecasts for the original index for each of the 20 days.
(b) Forecast the change in the index for each of the next 20 days by taking the average of the historical changes.
(a) Calculate the change in the index for each day by sub-tracting the value for the previous day. (This is known as \di®erencing" the data and is discussed in Chapter 6.)
2.7 Download the Dow Jones index from the web page and pro-duce a time plot of the series using a computer package.
(c) Repeat Part (b) using columns 1 and 3 below. Which forecasting method appears to be better?
(b) For each method, compute the Mean Error, Mean Abso-lute Error, Mean Squared Error, Mean Percentage Error, and Mean Absolute Percentage Error using equations(2.13) through (2.18).
(a) Plot the actual demand on a graph along with the fore-casts from the two methods.
2.6 Column 1 on the following page is the actual demand for prod-uct E15 over 20 months. Columns 2 and 3 are the one-month ahead forecasts according to two di®erent forecasting models to be
(d) Why is it inappropriate to calculate the autocorrelation of these data?
(c) Calculate the correlation of the two variables and pro-duce a scatterplot of Y against X.
(b) Which of these statistics give a measure of the center of data and which give a measure of the spread of data?
(a) Calculate the mean, median, MAD, MSD, and standard deviation for each variable.
2.5 Table 2-21 shows data on the performance of 14 trained female distance runners. The variables measured are the running time (minutes) in a 10 kilometer road race and the maximal aerobic power
2.4 In the graphs on the previous page, four time series are plotted along with their ACFs. Which ACF goes with which time series?
(e) Quarterly production of bricks (in millions of units) at Portland, Australia (March 1956{September 1994).
(d) Monthly total of accidental deaths in the United States(January 1973{December 1978).
(c) Number of lynx trapped annually in the McKenzie River district of northwest Canada (1821{1934).
(b) Daily morning temperature of a cow for 75 days.
(a) Monthly total of people on unemployed bene¯ts in Aus-tralia (January 1956{July 1992).
2.3 For each of the following series on the web page, make a graph of the data (using a computer package), describe the main features and, if transforming seems appropriate, do so and describe the
(d) Weekly electricity consumption for your local area over the past 10 years.\
(c) Daily sales at a fast-food store for six months.
(b) Hourly pulse rate of a person for one week.
(a) Monthly retail sales of computer disks for the past 10 years at your local store.
For each of the following series, what sort of time patterns would you expect to see?
(b) Make a time plot of the data. Is there any time pattern in the temperature readings?
(a) What is your best estimate of the average temperature in June 1995?
2.1 Table 2-20 gives average monthly temperatures in Paris.
Monthly milk production per cow over 14 years (Source: Cryer, 1986). The second graph shows the data adjusted for the length of month. This yields a simpler pattern enabling better forecasts and
Transformations of the electricity production data. Of these, either a square root, cube root, or a log transformation could be used to stabilize the variation to form a series which has variation
The electricity production data shown in Figure 1-2a (p. 7)exhibit a strong trend in addition to the monthly seasonality.The beer data in Figure 2-1 show no trend.Many data series include
4. A trend (T) pattern exists when there is a long-term increase or trend decrease in the data. The sales of many companies, the gross national product (GNP), and many other business or economic
3. A cyclical (C) pattern exists when the data exhibit rises and cyclical falls that are not of a ¯xed period. For economic series, these are usually due to economic °uctuations such as those
2. A seasonal (S) pattern exists when a series is in°uenced by seasonal seasonal factors (e.g., the quarter of the year, the month, or day of the week). Sales of products such as soft drinks, ice
1. A horizontal (H) pattern exists when the data values °uctuate horizontal around a constant mean. (Such a series is called \stationary"in its mean.) A product whose sales do not increase or
In the chapter example, we used a very small sample taken from two Usenet newsgroups (autos and electronics). Use the much larger data set that includes many postings from each of the two groups and

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