CHAPTER 11
Conclusion
Our class is approaching the end. Our professors are very anxious to summarize the important points so that the knowledge gained during this class will benefit the students for a lifetime.
Mo asks to tell us a story he saw on the Internet: “Aristotle (384–322 BC) raised the question of whether the chicken comes first or the egg comes first and concluded that both must have always existed. Thurman and Fisher (1988) tried to answer the question by performing a test using data on chickens that lay eggs except for commercial broilers and on eggs produced in the United States from 1930 to 1983. They found that the egg comes first.” He then asks, “Does that mean that the egg causes the chicken to come into existence?”
Dr. Theo thanks Mo for raising a good question. He says that this will be one of the topics discussed today but he first wants to summarize the techniques learned throughout this course.
Theoretical Summary
Dr. Theo’s summarization comprises two broad categories.
Pros and Cons of the Techniques
Moving Averages and Double Moving Averages—Chapters 2 to 4
Moving averages (MA) and double moving averages (DM) are the simplest techniques in forecasting. They are easy to implement and are the most cost-effective method, so they are good starting steps to forecasting. However, the simplicity of the models, including the weighted moving averages (WM) model with integer weights, might render inaccurate forecasts. The techniques usually produce a mean absolute percentage error (MAPE) of roughly 12 to 15 percent for one-period forecasts and 20 to 25 percent for four-period forecasts.
Exponential Smoothing and Double Exponential Smoothing—Chapters 2 to 4
These are more sophisticated techniques than the MAs because the weight (or weights in the double exponential smoothing [DE]) can be adjusted continuously from zero to one. Hence, the exponential smoothing (ES) technique often provides more accurate forecasts than the MA technique. However, the ES and DE models can only cover a limited range of data because they do not account for the seasonal and cyclical components of a time series. The techniques usually produce an MAPE of roughly 10 to 12 percent for one-period forecasts and 18 to 22 percent for four-period forecasts.
Advanced Time Series Analysis—Chapter 7
The decomposition and triple ES both incorporate the seasonal and cyclical components of a time series into their models and so can cover a wider range of data and longer-term forecasts than the preceding two techniques. The triple ES can even handle nonlinear trends, and the AR and ARMA/ARIMA models can handle a time series that follows a random walk. They are also able to reduce errors, with an MAPE of roughly 8 to 10 percent for one-period forecasts and 15 to 17 percent for four-period forecasts. Their weakness is that they still make forecasts based only on past performances of a time series.
Linear Regression Technique—Chapters 5 and 6
A widely applied technique in associative analyses, a linear regression, irrespective of whether it is simple or multiple linear regressions, often produces a smaller MAPE than those obtained from MA and ES techniques because the technique aims to minimize the errors (the least squared approach). Additionally, it takes into account more determinants of a market than the time series itself. A good linear regression model can produce an MAPE of roughly 8 to 10 percent for one-period forecasts and 15 to17 percent for four-period forecasts. However, when the relationship between the dependent variable and the explanatory ones are not linear in parameters, advanced knowledge of nonlinear regressions is needed to adjust the model accordingly.
Business Models—Chapter 8
These are very helpful models because they are developed specifically for businesses and have enjoyed wide applications in the business world. The running forecast model helps with inventory and ordering. The financial models help with investing, and the diffusion model is good for product adoption forecasts. The weakness of the running forecast model is that its applications are limited to inventory and ordering plans. The weakness of the other two groups is that the errors are large with an MAPE of roughly 14 to 18 percent for one-period forecasts and 20 to 25 percent for four-period forecasts.
Economic Models—Chapter 9
Between the two groups of the economic models, namely, production models and gravity models, the production models have a stronger base in economic theory. Hence, the production models produce smaller errors than the business models, with an MAPE of roughly 10 to 12 percent for one-period forecasts and 18 to 22 percent for four-period forecasts. The gravity models usually result in an MAPE’s range similar to that for business models. Their weakness lies in their applications, which are much more limited than those of the business models.
Business Cycles and Rates of Change—Chapter 10
The turning-point technique is popular in all disciplines whereas the models based on rates of change are currently used in the realm of public policy. However, they can be applied to a business environment, for example, forecasting a turning point of a business or catching-up games between two companies. Both groups are for long-term forecasts, but the models based on rates of change are for longer terms than the turning point models. The weakness of these models is that the errors are large, with an MAPE of roughly 15 to 20 percent for one-period forecasts, 20 to 25 percent for four-period forecasts, and 25 to 45 percent for 12-period forecasts.
Cautions on Forecast Results
Dr. Theo then emphasizes that there are several pitfalls to avoid.
Mistaking Correlation for Causality
This is the very issue raised by Mo about the chickens and the eggs. Dr. Theo explains that although the correlation between two variables makes them move in the same direction, stating that a variable X causes a variable Y to change is a common mistake in forecasting. In fact, variable X does not need to cause variable Y in order to help predict Y. Hence, producing a model that has predictive power is the most important goal in forecasting. Using a holdout sample is one way to test the predictive power of a model. The second way is to carry out an F-test on the regression model. The third way is to perform a Granger Causality test, which is the test on the chickens and the eggs mentioned by Mo.
Dr. Theo then says, “However, the fact that the egg comes first might not imply that the egg causes the chicken to come into existence. That is one of the reasons I did not teach the Granger Causality test in this class. Another reason is that I cannot teach a whole econometric course in a forecasting course. You can find details of the test in Ramanathan (1998) or Stock and Watson (2007), which are introductory textbooks in econometrics.”
We now understand Dr. Theo’s point: It is a good habit to make evaluations on the predictive power of a model, which is crucial, instead of focusing on the causal relation, which is not important, in making forecasts and discussing the forecast results.
Spurious Precision
Forecasters and decision makers are often confused between precision and accuracy. Due to the uncertainty of the future, all point forecasts carry large errors, especially when the forecasts are several periods away from the current one. Hence, interval forecasts should be more important than point forecasts, and a good forecaster should report a confidence interval instead of a single point. Use past experiences and current market conditions to make a decision on whether we should follow an upper or lower bound of an interval forecast for ordering inputs and delivering our products.
Theory-less Forecasting
Naïve forecasters may extrapolate past data without understanding any plausible theory behind them. For example using an AR(p) model without understanding the model structure and the conditions to use it can lead to a spurious regression due to nonstationarity. When this occurs, the results show strongly significant coefficients but the model still fails to predict the future. Hence, most sound forecasts are grounded not only in empiricism but also in theory. If the results seem to contradict a theory, a respecification process should be carried out to adjust the model.
Overreliance on Forecasts
Forecasters are sometimes subjective and can overestimate or underestimate the future. For example, a production manager, who holds an optimistic view of a company, can overestimate the forecast values. In contrast, a sales person who receives bonuses for his sales might underestimate the expected values so that his actual sales will exceed the forecasts in the future. For this reason, decision makers who take forecast values literally can be in for a great surprise. Thus, good decision makers should be cautious and communicate with related parties to adjust accordingly.
Ignoring Global Market Movements
The Financial Crisis of 2008–2009 revealed that the era of independent economies no longer exists. No matter how closed or strong an economy is and how sophisticated our forecast model, excluding international market movements might lead to huge errors in our results. We learn that we should utilize the Global Indicator Program provided by the Conference Board to assist us in understanding global financial conditions and adjusting our forecasts as analyzed in Manini and Ozyildirim (2013).
To conclude his remarks, Dr. Theo emphasizes that regardless of what we are trying to forecast, a combination of several quantitative techniques and qualitative judgments usually provides the best results.
Empirical Summary
Dr. App starts her section by sharing her experience in applying the forecast concepts into data analyses.
Data Issues
Collecting Data
If someone offers us a historical dataset, we are very lucky. In many instances, we have to search for one. To locate a dataset it is best to inquire within our company’s other departments, partner companies, or firms that we have to order inputs from, or firms to which we deliver outputs. We can also contact federal and local government offices. For example, Cita’s office has data on private firms in the city. We learn that we can also ask the Department of Energy, Department of Urban and Regional Planning, or the Department of Business and Economic Development in our city.
Dr. App then says, “In the worst situation, create your own dataset.”
At this point Arti offers her own experience, “Two years ago, before opening my art school, I conducted a quantitative survey by sending out survey forms asking people for specific values that they can fill in my questionnaires on their income, the number of children in their households, their preferences in visual and performing arts, and so on. Based on the information, I compiled a dataset for myself on the demand for instructions in the arts. I did not know how to forecast at that time, but I was able to perform some statistical analysis and came up with an estimate of the potential revenue for my school.”
Alte also raises her hand and says, “Last year, when I was considering to buy the alteration business at Alcorner, I went to the site and sat on a bench outside the store with a handful of my beads. Whenever a customer was walking out of the store with the store’s shopping bag, I moved a bead from my right pocket to my left one. At the end of the day, I multiplied the number of beads with a spending average of $10 for each paying customer to make one data point. I did this every day for two weeks as an approximation of the demand for alterations and came up with a dataset. I eventually decided to purchase the business.”
Dr. App thanks them for sharing their experiences with the class and moves on to the next subject. In the following section is what she says.
Cleaning the Data
Once you have successfully downloaded a dataset, do the following steps:
1.Eliminate all text except the labels on the top row.
2.For cross-sectional data or time series data, refer to Chapter 1 commands to transpose the data from horizontal to vertical arrangements.
3.For panel data: You can only transpose the time series section of each identity. You then copy and paste the time series for each identity gradually into Excel.
4.However, you can still refer to Chapter 1 to see how panel data should be organized.
5.Time series periods should be arranged from the lowest to the highest values. Refer to Chapter 1 for the sort commands.
6.A missing observation is often marked with a dot (.) or the letters N/A (nonapplicable). Delete the dot or the letters from the cell.
Missing Observations
Excel cannot handle missing observations. In cross-sectional data analyses, the best solution is to eliminate the observation completely. For example, suppose you want to regress productivity on education and investment. You have data on productivity and investment for 50 states and Washing, DC, but data on education for Washington, DC, is missing. The best course of action is to eliminate Washington, DC, completely from the data analyses.
In time series analysis, eliminating one period creates a gap in the series. For example, Mo wants to regress motorcycle sales on income and has data on motorcycle sales from January 2012 to December 2012, but data on the income of the city residents for June 2012 are missing. In this case, instead of eliminating data for June, the best strategy is to calculate an approximated value of the city resident income in June by averaging the income values in May and July. He can use this average to fill in the missing value for June.
Changing Units
We learn that if we only need to interpret the effect of an explanatory variable on the dependent variable while holding other variables constant, then the units of the explanatory variables should not matter. Since we need to calculate the predicted values in forecasting, we will have great difficulty if too many units are used. For example, if consumption is in dollars, income is in hundreds of dollars, and the stock prices are in thousands of dollars, then before calculating we will have to change the values of the coefficient estimates. Hence, changing all units into a single unit before performing regressions will make the calculations much easier.
Logarithmic Functions
Dr. App also reminds us that the logarithm of zero is undefined as shown in any college algebra textbook. Hence, if a cross-sectional dataset has a zero number, we can eliminate the data point before performing the regressions. If a time series dataset has a zero number, we can replace the zero with a small number. In order for the number to be small enough so that it does not bias the results, we need to scale up the dataset. For example, if the units are in thousands of dollars and the other values are in the range of 5 through 10, we can change them to dollars so that the values are in the range of 5,000 through 10,000 and then add 1.0 to the whole series so that 5,000 becomes 5,001 and the zero becomes 1.0.
Preliminary Analysis
Preliminary steps of data analysis such as sketching a time series plot and performing descriptive statistics before applying any forecast technique are very important. The fact that we obtain a reliable dataset does not imply that we can use all observations for estimations. For example, the maximum value in descriptive statistics might reveal an extremely high sale volume due to a recent promotion. This value will cause an overestimation of future sales. Any outlier should be eliminated before data analyses are performed. After a model is developed and forecast values are obtained, add these outliers back to the periods to which they belong. Other values reported in the descriptive statistics are also important as discussed in Chapter 1.
Technical Summary
Finally, Dr. App provides us with a summary table of all techniques introduced in this course and goes over each technique with us. Her table is displayed in Table 11.1.
Table 11.1 Summarization of methods learned in this course
| Technique | Using conditions | Remarks | Book sections | Illustrations Excel application |
| Part I: Basics | ||||
| Simple MA | Data exhibit neither seasonal nor cyclical components | Treating all periods with equal weight One-period forecasts |
Chapter 2, section on “Moving Averages” | Illustration: Figure 2.4 Data and commands: Ch02.xls, Fig. 2.4 |
| WM | Data exhibit neither seasonal nor cyclical components | Different weights are assigned using integers One-period forecasts |
Chapter 2, section on “Moving Averages” | Illustration: Figure 2.5 Data and commands: Ch02.xls, Fig. 2.5 |
| ES | Data exhibit neither seasonal nor cyclical components | One flexible weight 0 < a < 1 One-period forecasts |
Chapter 2, section on “Exponential Smoothing” |
Illustration: Figure 2.6 Data and commands: Ch02.xls, Fig. 2.6 |
| Part II: Intermediate Forecast Techniques | ||||
| DM | Data exhibit neither seasonal nor cyclical components | Combining two MAs and a trend equation Multiperiod forecasts |
Chapter 4, section on “Double Moving Average” | Illustrations: Table 4.1, and Figures 4.1, 4.2, and 4.3 Data and commands: Ch04.xls, Fig. 4.3 |
| DE | Data exhibit neither seasonal nor cyclical components | Two parameters E: 0 < a < 1 T: 0 < b < 1 Multiperiod forecasts |
Chapter 4, sections “Brown’s DE” and “Holt’s DE” under “Double Exponential Smoothing” | Illustrations: Tables 4.2 and 4.3; Figures 4.5, 4.6, and 4.7 Data and commands: Ch04.xls, Fig. 4.8 and Fig. 4.9 |
| Simple linear regressions | Data are stationary Six classic assumptions hold |
Number of explanatory variable: 1 Multiperiod forecasts |
Chapter 5, sections “Basic Concept” and “Predictions and Forecasts” | Illustrations: Table 5.1, Figures 5.1, 5.2, and 5.3 Data and commands: Ch05.xls, Fig. 5.2, Fig. 5.3, and Fig. 5.4 |
| Part III: Advanced Forecast Techniques | ||||
| Multiple linear regressions | Data are stationary Six classic assumptions hold |
Number of explanatory variables: two or more Multiperiod forecasts |
Chapter 6, sections “Basic Concept,” “Predictions and Forecasts,” and “Forecasts with Panel Data” |
Illustrations: Figures 6.1, 6.2, 6.3, 6.6, and 6.7 Data and commands: Ch06.xls, Fig. 6.2, Fig. 6.3, Fig. 6.6, and Fig. 6.7 |
| Decomposition | Data exhibit seasonal and cyclical components | Multiplicative model Multiperiod forecasts |
Chapter 7, section on “Decomposition” | Illustrations: Figures 7.1, 7.2, and 7.3 Data and commands: Ch07.xls, Fig. 7.1, Fig. 7.2, and Fig. 7.3 |
| Holt–Winters exponential smoothing (HWE) | Data exhibit seasonal and cyclical components | Three parameters: E: 0 < a < 1 T: 0 < b < 1 S: 0 < c < 1 |
Chapter 7, section on “Triple Exponential Smoothing” | Illustrations: Figure 7.4 Data and commands: Ch07.xls, Fig. 7.4 |
| Higher-order exponential smoothing (HOE) | Data are stationary | Three parameters One equation in polynomial or log form Linear in parameters |
Chapter 7, section on “Triple Exponential Smoothing” | Illustrations: Figures 7.5 and 7.6 Data and commands: Ch07.xls, Fig. 7.5 and Fig. 7.6 |
| AR (p), ARIMA (p, d, q) |
Stationary data: use original AR Random walk: use differenced models |
Univariate p = number of lagged dependent variables |
Chapter 7, section on “Brief Introduction to AR and ARIMA Models” | Illustrations: Table 7.7 and Figure 7.7 Data and commands: Ch07.xls, Fig. 7.8 |
| Part IV: Business and Economic Applications of Forecasting | ||||
| Operational forecasting | Demand forecasts are available as prerequisites | Forecasts of forecasts in a running process | Chapter 8, section on “Operational Forecasting” | Illustrations: Tables 8.1 and 8.2; Figure 8.1 Data and commands: Ch08.xls, Fig. 8.3 |
| Bond: yield to maturity (YTM) and interest rate forecasts (IRFs) | YTM: assumes constant i IRF: similar to regressions |
A guess and adjustment process on an Excel spreadsheet | Chapter 8, sections “Bond Markets” and “Excel Applications” under “Financial Forecast” | Illustrations: none Data and commands: Ch08.xls, Fig. 8.4 and Fig. 8.5 |
| Stock: expected returns and prices | CAPM and ATP models: similar to regressions DDM: constant growth rates of Π and D |
CAPM and ATP model: similar to regressions DDM: for short-run forecast only |
Chapter 8, sections “Stock Market” and “Excel Applications” under “Financial Forecast” | Illustrations: none Data and commands: Ch08.xls, Fig. 8.6 |
| Diffusion models: Bass and Lawrence–Lawton | Assumptions on shapes of pdf and cumulative distributions hold | Generate an entire product life cycle from several initial data points; for long-term forecasts | Chapter 8, section on “Diffusion Models on Sales and Demand” | Illustrations: Table 8.3 and Figures 8.5 and 8.6 Data and commands: Ch08.xls, Fig. 8.9 |
| Production forecasts | Profit maximization or cost minimization principles | Short-term forecasts on production allocations subject to resource constraints | Chapter 9, section on “Production Forecasts” | Illustrations: none Data and commands: Ch09.xls, Fig. 9.1, Fig. 9.2, Fig. 9.3, Fig. 9.4, and Fig. 9.5 |
| Gravity models | Physic principles of gravity between two objects | Short-term forecasts of efficient land-use and trip distributions | Chapter 9, section on “Gravity Models” |
Illustrations: Table 9.1 Data and commands: Ch09.xls, Fig. 9.7 |
| Turning points | Data on economic leading indicators are available | Long-term forecasts: current technique on diffusion indices gives equal weights to all indicators | Chapter 10, section on “Turning Points” | Illustrations: Tables 10.1 and 10.2 Data and commands: Ch10.xls, Fig. 10.2 and Fig. 10.4 |
| Rates of change: catching up or investment choices | Assumptions: all decisions depend on growth rates of profit, revenue, or investment | Long-term forecasts; four scenarios for catching-up games; more realistic with discount rates for investment choices | Chapter 10, section on “Models Based on Rates of Change” | Illustrations: Table 10.3 Data and commands: Ch10.xls, Fig. 10.6 and Fig. 10.7 |
Dr. Apps concludes her section by telling us that this textbook is an introduction to forecasting. Although it might be enough for simple problems, she hopes that we continue our learning in the future by reading more advanced books whenever we have the time. She also hopes that we combine the quantitative knowledge we have learned in this class with our common sense and qualitative judgment to obtain the best forecasts for our businesses.
We thank Dr. Theo and Dr. App for a course that has provided valuable knowledge that we can apply to our daily lives. Many of our classmates came to this country as political refugees with empty hands but have been doing quite well thanks to their entrepreneurial spirits, the determination to learn, and their eagerness to apply what they have learned into managing their businesses. We know that we can do the same.
It is time to say goodbye. We all wish the professors and each other good luck. We also wish you all the best for your future and hope that you have enjoyed this course as much as we have.