Forecasting Methods And Applications 3rd Edition Spyros G. Makridakis, Steven C. Wheelwright, Rob J Hyndman - Solutions

(f) If you have access to a suitable computer package, ¯t a local linear regression to these data. You will need to try several bandwidths and select the one which looks most appropriate. What does the ¯tted curve suggest about the two models?
(e) For each model, ¯nd the value of R2 and produce a residual plot. Comment on the adequacy of the two models.
(d) Fit the two models and ¯nd the coe±cients, and residual variance in each case. For the ¯rst model, use (5.15) to estimate the residual variance. But for the second model, because there are four parameters, the residual degrees of freedom is n ¡ 4. So the residual variance ¾2" can be
(c) The data are clearly not linear. Two possible nonlinear models for the data are given below exponential model piecewise linear model Yi = exp(a + bXi + ei)Yi =(a1 + b1Xi + ei when Xi · 60 a2 + b2Xi + ei when Xi > 60.The second model divides the data into two sections, depending on whether the
(b) Plot these data on a graph with consumption as the Y -axis and price as the X-axis.
(a) Are these cross-sectional or time series data?
5.10 Table 5-10 shows a data set consisting of the demand for natural gas and the price of natural gas for 20 towns in Texas in 1969.
(e) One poultry farmer tells you that he tends to use higher proportions of Type A birds in summer because they are better adapted to the Australian heat. How does this information alter your interpretation of the results?
(d) What proportion of variation in mortality can be as-cribed to bird type?
(e) Transform your predictions and intervals to obtain pre-dictions and intervals for the raw data.
(d) Use your regression model to predict the logarithm of the total annual sales for 1994, 1995, and 1996. Produce prediction intervals for each of your forecasts.
(c) Calculate total sales each year and ¯nd the logarithms of these sales. Plot these against the year and ¯t a linear regression line to these data.
(b) Explain why it is necessary to take logarithms of these data before ¯tting a model.
(a) Produce a time plot of the data and describe the pat-terns in the graph. Identify any unusual or unexpected°uctuations in the time series.
5.8 The data in Table 5-8 concern the monthly sales ¯gures of a shop which opened in January 1987 and sells gifts, souvenirs, and novelties. The shop is situated on the wharf at a beach resort town in Queensland, Australia. The sales volume varies with the seasonal population of tourists. There is
(c) Plot the residuals against the year. What does this indicate about the suitability of the ¯tted line?
(b) Fit a regression line to the data. Obviously the winning times have been decreasing, but at what average rate per year?
(a) Plot the winning time against the year. Describe the main features of the scatterplot.
5.7 Table 5-7 gives the winning times (in seconds) for the men's 400 meters ¯nal in each Olympic Games from 1896 to 1996.
(c) What can you conclude generally about the impact of such outliers on r?
(b) Imagine that the King Kong data were H = 40 and W =150 (a short fat King Kong!) and recompute rHW.
(a) Imagine that the King Kong data added to the 20 normal gorillas were H = 130 and W = 45 (a very skinny King Kong!) and recompute rHW.
5.6 Figure 5-8 (p. 198) presents the King Kong data set and shows how strong the in°uence of one outlier can be in determining the correlation coe±cient.
(d) Use the model to predict the electricity consumption that you would expect for a day with maximum temperature 10± and a day with maximum temperature 35±. Do you believe these predictions?
(c) Produce a residual plot. Is the model adequate? Are there any outliers or in°uential observations?
(b) Find the correlation coe±cient, r.
(a) Plot the data and ¯nd the regression model for Mwh with temperature as an explanatory variable. Why is there a negative relationship?
5.5 Electricity consumption was recorded for a small town on 12 randomly chosen days. The following maximum temperatures(degrees Celsius) and consumption (megawatt-hours) were recorded for each day.Day 1 2 3 4 5 6 7 8 9 10 11 12 Mwh 16.3 16.8 15.5 18.2 15.2 17.5 19.8 19.0 17.5 16.0 19.6 18.0 temp
(d) Determine the 95% con¯dence interval for the slope co-e±cient in the regression equation.
(c) If a test score was 80, what would be your forecast of the production rating? What is the standard error of this forecast?
(b) Compute the coe±cients of the linear regression of Y on X, and examine the signi¯cance of the relationship.
(a) Plot these data on a graph with test score as the X-axis and production rating as the Y -axis.
(e) Explain the assumptions and limitations in your predic-tion. What other factors may play a role?
(d) In 1993, scientists discovered that 40% of ozone was depleted in the region of Hamburg, Germany. What would you expect to be the rate of melanoma in this area? Give a prediction interval.
(c) What percentage of the variation in rates of melanoma is explained by the regression relationship?
(b) Plot the residuals from your regression against ozone depletion. What does this say about the ¯tted model?
(a) Plot melanoma against ozone depletion and ¯t a straight line regression model to the data.
The following data are ozone depletion rates in various loca-tions and the rates of melanoma (a form of skin cancer) in these locations.Ozone dep (%) 5 7 13 14 17 20 26 30 34 39 44 Melanoma (%) 1 1 3 4 6 5 6 8 7 10 9
5.3 Skin cancer rates have been steadily increasing over recent years. It is thought that this may be due to ozone depletion.
(a) Determine the linear regression line relating Y to X.
5.2 Suppose the following data represent the total costs and the number of units produced by a company.Total Cost Y 25 11 34 23 32 Units Produced X 5 2 8 4 6
25. How can you explain the negative correlation?
(e) A survey in 1960 showed a correlation of r = ¡0:3 between age and educational level for persons aged over
(d) A positive correlation between in°ation and unemploy-ment is observed. Does this indicate a causal connection or can it be explained in some other way?
explain the association between AWE and new houses in some other way?
(c) A study ¯nds an association between the number of new houses built and average weekly earnings (AWE). Should you conclude that AWE causes new houses? Or can you
(b) If the correlation coe±cient is ¡0:75, below-average val-ues of one variable tend to be associated with below-average values of the other variable. True or false?Explain.
² If the F statistic is between the middle value and the last value, then the P-value is between 0.01 and 0.05.
² If the F statistic is between the ¯rst value and the middle value, then the P-value is between 0.05 and 0.10.
² If the F statistic is smaller than the ¯rst value, then the P-value is bigger than 0.10.
a normal distribution.
3. The error terms "i all have mean zero and variance ¾2" , and have
2. The error terms "i are uncorrelated with one another.
1. The explanatory variable Xi takes values which are assumed to be either ¯xed numbers (measured without error), or they are random but uncorrelated with the error terms "i. In either
2. The magnitude of the correlation coe±cient is a measure of the strength of the association|meaning that as the absolute value
1. The sign of the correlation coe±cient (+ or ¡) indicates the direction of the relationship between the two variables. If it is positive, they tend to increase and decrease together; if it is negative, one increases while the other decreases; if it is close to zero, they move their separate
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 parameters, and compute the one-ahead forecasts. Check the error statistics for the test period 10{24 and
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, additive Holt-Winters method, and multiplicative Holt-Winters 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 combination with ¯ values of 0.1, 0.3, and 0.5. What role does¯ play in ARRSES?
(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 books.
(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 11- month moving average?
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 46 Sep 30 Oct 66 Nov 80 Dec 89
(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 5.3 3 5.3 4 5.6 1975 1 6.9 2 7.2 3 7.2
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 last period's observation as the forecast for the next period. In row 3 the SES model is seen to be
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 alternating with runs of negative errors, then r1 is much greater than 0(approaching an upper limit of 1).
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 MAE and minimum MAPE values. This is not always the case and sometimes an alternative method might be
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 1126 Apr 898 932 1055 1109 1285 May 1030 1099 1204 1274 1468 Jun 1107 1223 1326 1422 1637 Jul 1165
(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.

Showing 1000 - 1100 of 1262

Forecasting Methods And Applications 3rd Edition Spyros G. Makridakis, Steven C. Wheelwright, Rob J Hyndman - Solutions

Step by Step Answers