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1.4 Organization of the Thesis
This thesis is organized into five chapters. Chapter 1 is the introduction of this paper. Chapter 2 presents the literature review and some comments. Chapter 3 describes and discusses the models in this study. Chapter 4 covers data analysis and finds. Finally, Chapter 5 summarizes conclusions, implications, and future research.
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CHAPTER 2 Literature Review
Forecasting techniques have been discussed and classified by researchers (Small,1980;
Georgoff and Murdick, 1986; Rao and Cox, 1987; Bails, Peppers, 1993; Bolt, 1994; Mentzer and Kahn, 1995; Peterson and Lewis, 1999; Cox and Loomis, 2001).Johnston and Marshall (2003) summarized some advantages and limitations of the various forecasting methods.
Scott Armstrong (2001) developed one hundred and thirty-nine principles for forecasting, which include defining a problem, collecting information about it, selecting and applying methods, evaluating methods, and deriving forecasts. Later, Armstrong (2005) summarized nine generalizations that can improve forecast accuracy. In his article, Scott Armstrong suggested on how to formulate a forecasting problem, how to tap managers’ knowledge, and how to select appropriate forecasting methods.
Furthermore, Armstrong (2010) developed a very useful Methodology Tree (see Figure 1) for forecasting which classifies all possible types of forecasting methods into categories and shows how they relate to one another.
The content of the Methodology Tree are summarized as follows:
Causal models: Theory, prior research and expert domain knowledge are used to specify relationships between a variable to be forecast and explanatory variables.
Classification: If the problem is composed of groups that act in different ways in response to a change, one can study each group separately, then add across segments.
Conjoint analysis: Elicit preferences from consumers for various offerings by using
combinations of features. Regression-like analyses are then used to predict the most desirable design.
Data-based: Experience and prior research are not available and so one must try to infer relationships from the data.
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Data mining: Letting the data speak for themselves. In general, theory is not considered.
Despite its widespread use and many claims of accuracy, we have been unable to find
evidence that data mining provides forecasts that are more accurate than those from alternative methods.
Figure 1: Methodology tree for forecasting (Forecastingprinciples.com)
Decomposition: Decomposition is a method for dealing with such problems by breaking down (decomposing) the estimation task down into a set of components that can be more readily estimated, and then combining the component estimates to produce a target estimate.
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Expert Forecasting refers to forecasts obtained in a structured way from two or more experts.
Expert systems: Rules for forecasting are derived from the reasoning experts use when making forecasts. Obtain knowledge from diverse sources such as surveys, interviews, protocol analysis, and research papers.
Extrapolation: Use time-series data, or similar cross-sectional data, to predict.
Index: In situations with many causal variables and few observations, the forecaster can nevertheless often use prior domain knowledge to assess the directional influence of individual variables on the outcome. The values of explanatory variables can be assessed subjectively, for example as zero or one, or can be normalized quantitative data where available. An index forecast is the sum of the values of the explanatory variables.
Intentions/expectations/experimentation: Survey people about their intentions or
expectations regarding their future behavior or those of their organization. Analyze the survey data to derive forecasts. Conduct an experiment by changing key causal variables in a
systematic way such that the independent variables are not correlated with one another.
Estimate relationships from responses to the changes and use these estimates to derive forecasts. Experiments can be used to predict the effects of different policies or regulatory schemes, or to assess the effectiveness of alternative advertisements.
Judgmental: Available data are inadequate for quantitative analysis or qualitative information is likely to increase accuracy, relevance, or acceptability of forecasts.
Judgmental bootstrapping: Derive a model from knowledge of experts’ forecasts and the factors they used to make their forecasts using regression analysis.
Knowledge source: When reliable objective data are available, they should be used. Still, one might benefit from also using subjective methods.
Linear: The problem can be modeled as linear in the parameters.
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Multivariate: Data are available on variables that might affect the behaviour of interest.
No role: Roles are not expected to influence behavior, or knowledge about the roles is lacking, or there are many actors with different roles.
Others: Knowledge exists about the expected behavior of other people or organizations.
Quantitative analogies: Experts identify analogous situations for which time-series or cross-sectional data are available, and rate the similarity of each analogy to the data-poor target situation. These inputs are used to derive a forecast.
Regression analysis: Sometimes referred to as “econometric modeling”, forecasting using models with parameters estimated from historical data using statistical techniques is, however, widely relevant.
Role: People's roles influence their behaviors and there is knowledge about these roles.
Role playing/Simulated interaction: In role playing, people are expected to think in ways consistent with the role and situation described to them. If this involves interacting with people with different roles for the purpose of predicting the behavior of actual protagonists, we call it simulated interaction. That is, people act out prospective interactions in a realistic manner. The role-players' decisions are used as forecasts of the actual decision.
Rule-based forecasting: Expert domain knowledge and statistical techniques are combined using an expert system to extrapolate time series. Most series features are identified by automated analysis, but experts identify some factors. In particular they identify the causal forces acting on trends.
Segmentation: Where a heterogeneous whole can be divided into parts that act in different ways in response to changes, that are relatively homogenous, and that can be forecast more accurately than can the whole.
Self: People have valid intentions or expectations about their behavior. Both are most useful when (1) responses can be obtained from a representative sample, (2) responses are based on good knowledge, (3) there are no reasons to lie, (4) new information is unlikely to change the
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behavior. Intentions are more limited than expectations in that they are most useful when (5) the event is important, (6) the behavior is planned, and (7) the respondent can fulfill the plan (so, for example, the behavior is not dependent on the agreement of other people.
Statistical: Relevant numerical data are available.
Structured: Formal methods are used to analyze the information. This means that the rules for analysis are written in advance and they are rigorously adhered to. Records should be kept of how the procedures were administered.
Structured analogies: An expert lists analogies to a target, describes similarities and
differences, rates similarity, and matches each analogy's decision (or outcome) with a potential target situation decision (or outcome). The outcome implied by the top-rated analogy is used as a forecast.
Theory-based: Experience and prior research provide useful information about relationships relevant to the forecast.
Unaided judgment: Experts think about a situation and predict how people will behave. They might have access to data and advice, but their forecasts are not aided by formal forecasting methods. This is the most commonly used method. It is fast, inexpensive when only a few forecasts are needed, and can be used in cases where small changes are expected. It is most likely to be useful when the forecaster gets good feedback about the accuracy of his forecasts (e.g., weather forecasting, betting on sports, and bidding in bridge games.)
Univariate :Historical data are available on the behaviour that is to be predicted.
Unstructured: The information is used in an informal manner.
Many researchers have investigated the classification criteria for forecasting methods such as Clemen(1989), McGuiganandMoyler (1989),BailsandPerpers (1993), Bolt (1994), Hall
(1994),Taylor (1996), Kinnear, Reekie, and Crook (1998), Makridakis and Wheelwright(1998), Kennedy (1999), Peterson and Lewis (1999), Kirsten (2000), Goodwin (2002), LarrickandSoll (2006), Green and Armstrong (2007).
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Decomposition is a method designed for solving this kind of problems by breaking down (decomposing) the forecasting task into a set of components that can be more readily estimated, and then combining the component estimates to produce a target estimate
(Armstrong,2001). Persons (1919, 1923) started the research on decomposing a seasonal time series. Since then, many forecasters had devoted to developing forecasting methods to predict data time series with trend and seasonality. Those methods include Decomposition, Winters exponential smoothing, Time series regression, and ARIMA models (Bowerman and O’Connell, 1993; Hanke and Reitsch, 1995).
Winters multiplicative seasonal trend model, one of the most popular forecasting models, was first developed by Charles C. Holt. Then, Peter R. Winters extended the model to forecast the seasonal demands. (Holt, 1957; Winters, 1960). Later, Box and Jenkins (1976) extended Holt-Winters model to the seasonal ARIMA model. The applications of ARIMA model are well adopted by the industries. (Kurawarwala and Matsuo, 1998; Hyndman, 2004)
Neural Networks (NN) models are also used for time series forecasting ( Hill, O’Connor and Reus, 1996; Faraway and Chatfield,1998; Zhang et al., 1998; Nelson et al., 1999; Hansen and Nelson, 2003; Yamaha and Eurasia, 1991;A.N. Refenes,1993;White,1988; Kamijo and Tanigawa,1990; Kimoto and Asakawa,1990; Schoeneburg, 1990; Hearing, 2006;Chang,Liu and Fan,2009; Chang, et al.,2009; Chang, et al., 2009).
Suhartono, et al. (2005) compare some forecasting methods including Decomposition, Winters, Time Series Regression, ARIMA and Neural Networks models. In this empirical research, their focus is to study whether a complex method always give a better forecast than a simpler method. A real time series data of airline passenger was performed on these models. The findings show that the more complex model does not always yield a better result than a simpler one.
Little research compared the forecasts of the market sales of seasonal products (such as ice cream, fresh milk, and air conditioner) in Taiwan, betweentheWinters Model and
Decomposition Model. Therefore, it creates the motive of this research.
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This study tries to compare the performance of the Winters Model and the Decomposition Model for seasonal consumer products in Taiwan, using ice cream, fresh milk, and air conditioner as examples, to determine the better forecasting model. Through the validation process, the best method is to be selected based on the minimum Mean Square Error.
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CHAPTER 3
Two Forecasting Models for the Seasonal Demand
Two forecasting models to predict seasonal market sales of ice cream, fresh milk, and air conditioner in Taiwan will be presented in this chapter—including theWinter’s multiplicative trend seasonal model and the Decomposition method. The two forecasting models are
presented as follows.