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Forecasting

Forecasting

QUALITATIVE TECHNIQUES
QUANTITATIVE TECHNIQUES
ECONOMETRIC FORECASTING
EVALUATING FORECASTS
MAKING A FORECAST
BIBLIOGRAPHY

Forecasting involves the generation of a number, set of numbers, or scenario that corresponds to a future occurrence. It is absolutely essential to short-range and long-range planning. By definition, a forecast is based on past data, as opposed to a prediction, which is more subjective and based on instinct, gut feel, or guess. For example, the evening news gives the weather forecast, not the weather prediction. Therefore, forecasts should not be mistaken for predictions because forecasting is based on traceable and observable data and trends as opposed to mere assumptions. Properly prepared forecasts should be able to address blips that arise from one-off spread factors as well as other major seasonal factors. Spreadsheets can be used for analyzing past trends and determining forecasts.

Forecasting is based on a number of assumptions:

  1. The past will repeat itself. In other words, what has happened in the past will happen again in the future.
  2. As the forecast horizon shortens, forecast accuracy increases. For instance, a forecast for tomorrow will be more accurate than a forecast for next month; a forecast for next month will be more accurate than a forecast for next year; and a forecast for next year will be more accurate than a forecast for ten years in the future.
  3. Forecasting in the aggregate is more accurate than forecasting individual items. This means that a company will be able to forecast total demand over its entire spectrum of products more accurately than it will be able to forecast individual stock-keeping units. For example, General Motors can more accurately forecast the total number of cars needed for next year than the total number of white Chevrolet Impalas with a certain option package.
  4. Forecasts are seldom accurate and almost never totally accurate, although some are very close. Therefore, it is wise to offer a forecast range. If one were to forecast a demand of 100,000 units for the next month, it is extremely unlikely that demand would equal exactly 100,000. However, a forecast of 90,000 to 110,000 would provide a much larger target for planning.

William J. Stevenson lists a number of characteristics that are common to a good forecast:

  • Accuratesome degree of accuracy should be determined and stated so that comparison can be made to alternative forecasts.
  • Reliablethe forecast method should consistently provide a good forecast if the user is to establish some degree of confidence.
  • Timelya certain amount of time is needed to respond to the forecast so the forecasting horizon must allow for the time necessary to make changes.
  • Easy to use and understandusers of the forecast must be confident and comfortable working with it.
  • Cost-effectivethe cost of making the forecast should not outweigh the benefits obtained from the forecast.

Forecasting techniques range from the simple to the extremely complex. These techniques are usually classified as being qualitative or quantitative.

QUALITATIVE TECHNIQUES

Qualitative forecasting techniques are generally more subjective than quantitative forecasting techniques. Qualitative techniques are more useful in the earlier stages of the product life cycle, when less past data exists for use in quantitative methods. Qualitative methods include the Delphi technique, Nominal Group Technique (NGT), sales force opinions, executive opinions, and market research.

The Delphi Technique. The Delphi technique uses a panel of experts to produce a forecast. Each expert is asked to provide a forecast specific to the need at hand. After the initial forecasts are made, each expert reads what every other expert wrote and is influenced by their views. A subsequent forecast is then made by each expert. Each expert then reads again what every other expert wrote and is again influenced by the perceptions of the others. This process repeats itself until each expert nears agreement on the needed scenario or numbers.

Nominal Group Technique. The Nominal Group technique is similar to the Delphi technique in that it utilizes a group of participants, usually experts. After the participants respond to forecast-related questions, they rank their responses in order of perceived relative importance. Then the rankings are collected and aggregated. Eventually, the group should reach a consensus regarding the priorities of the ranked issues.

Sales Force Opinions. The sales staff is often a good source of information regarding future demand. The sales manager may ask for input from each salesperson and aggregate their responses into a sales force composite forecast. Caution should be exercised when using this technique as the members of the sales force may not be able to distinguish between what customers say and what they actually do. Also, if the forecasts will be used to establish sales quotas, the sales force may be tempted to provide lower estimates.

Executive Opinions. Sometimes upper-level managers meet and develop forecasts based on their knowledge of their areas of responsibility. This is sometimes referred to as a jury of executive opinion.

Market Research. In market research, consumer surveys are used to establish potential demand. Such market research usually involves constructing a questionnaire that solicits personal, demographic, economic, and marketing information. On occasion, market researchers collect such information in person at retail outlets and malls, where the consumer can experiencetaste, feel, smell, and seea particular product. The researcher must be careful that the sample of people surveyed is representative of the desired consumer target.

QUANTITATIVE TECHNIQUES

Quantitative forecasting techniques are generally more objective than qualitative forecasting methods. Quantitative forecasts can be time-series forecasts (i.e., a projection of the past into the future) or forecasts based on associative models (i.e., based on one or more explanatory variables). Time-series data may have underlying behaviors that need to be identified by the forecaster. In addition, the forecast may need to identify the causes of the behavior. Some of these behaviors may be patterns or simply random variations. Among the patterns are:

  • Trends, which are long-term movements (up or down) in the data.
  • Seasonality, which produces short-term variations that are usually related to the time of year, month, or even a particular day, as witnessed by retail sales at Christmas or the spikes in banking activity on the first of the month and on Fridays.
  • Cycles, which are wavelike variations lasting more than a year that are usually tied to economic or political conditions.
  • Irregular variations that do not reflect typical behavior, such as a period of extreme weather or a union strike.
  • Random variations, which encompass all non-typical behaviors not accounted for by the other classifications.
Table 1
Naïve Forecasting
Period Actual Demand (000's) Forecast (000's)
January 45  
February 60 45
March 72 60
April 58 72
May 40 58
June   40

Among the time-series models, the simplest is the naïve forecast. A naïve forecast simply uses the actual demand for the past period as the forecasted demand for the next period. This makes the assumption that the past will repeat. It also assumes that any trends, seasonality, or cycles are either reflected in the previous period's demand or do not exist. An example of naïve forecasting is presented in Table 1.

Another simple technique is the use of averaging. To make a forecast using averaging, one simply takes the average of some number of periods of past data by summing each period and dividing the result by the number of periods. This technique has been found to be very effective for short-range forecasting.

Variations of averaging include the moving average, the weighted average, and the weighted moving average. A moving average takes a predetermined number of periods, sums their actual demand, and divides by the number of periods to reach a forecast. For each subsequent period, the oldest period of data drops off and the latest period is added. Assuming a three-month moving average and using the data from Table 1, add 45 (January), 60 (February), and 72 (March) and divide by three to arrive at a forecast for April:

45 + 60 + 72 = 177 ÷ 3 = 59

To arrive at a forecast for May, drop January's demand from the equation and add the demand from April. Table 2

Table 2
Three Month Moving Average Forecast
Period Actual Demand (000's) Forecast(000's)
January 45  
February 60  
March 72  
April 58 59
May 40 63
June   57

presents an example of a three-month moving average forecast.

A weighted average applies a predetermined weight to each month of past data, sums the past data from each period, and divides by the total of the weights. If the forecaster adjusts the weights so that their sum is equal to 1, then the weights are multiplied by the actual demand of each applicable period. The results are then summed to achieve a weighted forecast. Generally, the more recent the data is, the higher the weight, and the older the data the smaller the weight. Using the demand example, a weighted average using weights of.4,.3,.2, and.1 would yield the forecast for June as:

60(.1) + 72(.2) + 58(.3) + 40(.4) = 53.8

Forecasters may also use a combination of the weighted average and moving average forecasts. A weighted moving average forecast assigns weights to a predetermined number of periods of actual data and computes the forecast the same way as described above. As with all moving forecasts, as each new period is added, the data from the oldest period is discarded. Table 3 shows a three-month weighted moving average forecast utilizing the weights.5,.3, and.2.

A more complex form of weighted moving average is exponential smoothing, so named because the weight falls off exponentially as the data ages. Exponential smoothing takes the previous period's forecast and adjusts it by a predetermined smoothing constant,α (called alpha; the value for alpha is less than one) multiplied by the difference in the previous forecast and the demand that actually occurred during the previously forecasted period (called forecast error). Exponential smoothing is expressed formulaically as such:

New forecast = previous forecast + alpha (actual demand previous forecast) F = F +ά (AF)

Exponential smoothing requires the forecaster to begin the forecast in a past period and work forward to the period for which a current forecast is needed. A substantial amount of past data and a beginning or initial forecast are also necessary. The initial forecast can be an actual forecast from a previous period, the actual demand from a previous period, or it can be estimated by averaging all or part of the past data. Some heuristics exist for computing an initial forecast. For example, the heuristic N = (2 ÷ α) 1 and an alpha of.5 would yield an N of 3, indicating the user would average the first three periods of data to get an initial forecast. However, the accuracy of the initial forecast is not critical if one is using large amounts of data, since exponential smoothing is self-correcting.

Table 3
Three-Month Weighted Moving Average Forecast
Period Actual Demand (000's) Forecast (000's)
January 45  
February 60  
March 72  
April 58 55
May 40 63
June   61

Given enough periods of past data, exponential smoothing will eventually make enough corrections to compensate for a reasonably inaccurate initial forecast. Using the data used in other examples, an initial forecast of 50, and an alpha of.7, a forecast for February is computed as such:

New forecast (February) = 50 +.7(45 50) = 41.5

Next, the forecast for March:

New forecast (March) = 41.5 +.7(60 41.5) = 54.45

This process continues until the forecaster reaches the desired period. In Table 4 this would be for the month of June, since the actual demand for June is not known.

An extension of exponential smoothing can be used when time-series data exhibits a linear trend. This method is known by several names: double smoothing; trend-adjusted exponential smoothing; forecast including trend; and Holt's Model. Without adjustment, simple exponential smoothing results will lag the trend; that is, the forecast will always be low if the trend is increasing, or high if the trend is decreasing. With this model there are two smoothing constants,α and β with β representing the trend component.

An extension of Holt's Model, called Holt-Winter's Method, takes into account both trend and seasonality.

Table 4
Period Actual Demand (000's) Forecast (000's)
January 45 50
February 60 41.5
March 72 54.45
April 58 66.74
May 40 60.62
June   46.19

There are two versions, multiplicative and additive, with the multiplicative being the most widely used. In the additive model, seasonality is expressed as a quantity to be added to or subtracted from the series average. The multiplicative model expresses seasonality as a percentageknown as seasonal relatives or seasonal indexesof the average (or trend). These are then multiplied times values in order to incorporate seasonality. A relative of 0.8 would indicate demand that is 80 percent of the average, while 1.10 would indicate demand that is 10 percent above the average. Detailed information regarding this method can be found in most operations management textbooks or one of a number of books on forecasting.

Associative or causal techniques involve the identification of variables that can be used to predict another variable of interest. For example, interest rates may be used to forecast the demand for home refinancing. Typically, this involves the use of linear regression, where the objective is to develop an equation that summarizes the effects of the predictor (independent) variables upon the forecasted (dependent) variable. If the predictor variable were plotted, the object would be to obtain an equation of a straight line that minimizes the sum of the squared deviations from the line (with deviation being the distance from each point to the line). The equation would appear as: y = a + bx, where y is the predicted (dependent) variable, x is the predictor (independent) variable, b is the slope of the line, and a is equal to the height of the line at the y-intercept. Once the equation is determined, the user can insert current values for the predictor (independent) variable to arrive at a forecast (dependent variable).

If there is more than one predictor variable or if the relationship between predictor and forecast is not linear, simple linear regression will be inadequate. For situations with multiple predictors, multiple regression should be employed, while non-linear relationships call for the use of curvilinear regression.

ECONOMETRIC FORECASTING

Econometric methods, such as autoregressive integrated moving-average model (ARIMA), use complex mathematical equations to show past relationships between demand and variables that influence the demand. An equation is derived and then tested and fine-tuned to ensure that it is as reliable a representation of the past relationship as possible. Once this is done, projected values of the influencing variables (income, prices, etc.) are inserted into the equation to make a forecast.

EVALUATING FORECASTS

Forecast accuracy can be determined by computing the bias, mean absolute deviation (MAD), mean square error

(MSE), or mean absolute percent error (MAPE) for the forecast using different values for alpha. Bias is the sum of the forecast errors [Σ(FE)]. For the exponential smoothing example above, the computed bias would be:

(60 41.5) + (72 54.45) + (58 66.74) + (40 60.62) = 6.69

If one assumes that a low bias indicates an overall low forecast error, one could compute the bias for a number of potential values of alpha and assume that the one with the lowest bias would be the most accurate. However, caution must be observed in that wildly inaccurate forecasts may yield a low bias if they tend to be both over forecast and under forecast (negative and positive). For example, over three periods a firm may use a particular value of alpha to over forecast by 75,000 units (-75,000), under forecast by 100,000 units (+100,000), and then over forecast by 25,000 units (-25,000), yielding a bias of zero (-75,000 + 100,000 25,000 = 0). By comparison, another alpha yielding over forecasts of 2,000 units, 1,000 units, and 3,000 units would result in a bias of 5,000 units. If normal demand was 100,000 units per period, the first alpha would yield forecasts that were off by as much as 100 percent while the second alpha would be off by a maximum of only 3 percent, even though the bias in the first forecast was zero.

A safer measure of forecast accuracy is the mean absolute deviation (MAD). To compute the MAD, the forecaster sums the absolute value of the forecast errors and then divides by the number of forecasts (Σ |FE| ÷N). By taking the absolute value of the forecast errors, the offsetting of positive and negative values are avoided. This means that both an over forecast of 50 and an under forecast of 50 are off by 50. Using the data from the exponential smoothing example, MAD can be computed as follows:

(|60 41.5| + |72 54.45| + |58 66.74| + |40 60.62|) ÷ 4 = 16.35

Therefore, the forecaster is off an average of 16.35 units per forecast. When compared to the result of other alphas, the forecaster will know that the alpha with the lowest MAD is yielding the most accurate forecast.

Mean square error (MSE) can also be utilized in the same fashion. MSE is the sum of the forecast errors squared divided by N-1 [Σ(P(FE)) ÷ (N-1)]. Squaring the forecast errors eliminates the possibility of offsetting negative numbers, since none of the results can be negative. Utilizing the same data as above, the MSE would be:

[(18.5) + (17.55) + (8.74) + (20.62)] ÷ 3 = 383.94

As with MAD, the forecaster may compare the MSE of forecasts derived using various values of alpha and assume the alpha with the lowest MSE is yielding the most accurate forecast.

The mean absolute percent error (MAPE) is the average absolute percent error. To arrive at the MAPE one must take the sum of the ratios between forecast error and actual demand times 100 (to get the percentage) and divide by N[(Σ | Actual demand forecast | ÷Actual demand) × 100 ÷ N]. Using the data from the exponential smoothing example, MAPE can be computed as follows:

[(18.5/60) + 17.55/72 + 8.74/58 + 20.62/48) × 100] ÷ 4 = 28.33%

As with MAD and MSE, the lower the relative error the more accurate the forecast.

It should be noted that in some cases the ability of the forecast to change quickly to respond to changes in data patterns is considered to be more important than accuracy. Therefore, one's choice of forecasting method should reflect the relative balance of importance between accuracy and responsiveness, as determined by the forecaster.

MAKING A FORECAST

William J. Stevenson lists the following as the basic steps in the forecasting process:

  • Determine the forecast's purpose. Factors such as how and when the forecast will be used, the degree of accuracy needed, and the level of detail desired determine the cost (time, money, employees) that can be dedicated to the forecast and the type of forecasting method to be utilized.
  • Establish a time horizon. This occurs after one has determined the purpose of the forecast. Longer-term forecasts require longer time horizons and vice versa. Accuracy is again a consideration.
  • Select a forecasting technique. The technique selected depends upon the purpose of the forecast, the time horizon desired, and the allowed cost.
  • Gather and analyze data. The amount and type of data needed is governed by the forecast's purpose, the forecasting technique selected, and any cost considerations.
  • Make the forecast.
  • Monitor the forecast. Evaluate the performance of the forecast and modify, if necessary.
  • Establish cause and effect relationships that add validation to a forecast.

SEE ALSO Futuring; Manufacturing Resources Planning; Planning; Sales Management

BIBLIOGRAPHY

Finch, Byron J. Operations Now: Profitability, Processes, Performance. 2nd ed. Boston: McGraw-Hill Irwin, 2006.

Forecasting Principles forecastingprinciples.com. Available from: http://www.forecastingprinciples.com.

Green, William H. Econometric Analysis. 5th ed. Upper Saddle River, NJ: Prentice Hall, 2003.

Hanke, John E. and Dean Wichern. Business Forecasting. 9th ed. Upper Saddle River, NJ: Prentice Hall, 2008.

Joppe, Dr. Marion. The Nominal Group Technique The Research Process. Available from: http://www.ryerson.ca/mjoppe/ResearchProcess/841TheNominalGroupTechnique.htm.

Stevenson, William J. Operations Management. 8th ed. Boston: McGraw-Hill Irwin, 2005.

Stutely, R. Definitive Guide to Business Finance: What Smart Managers Do with the Numbers. Prentice Hall: Upper Saddle River, New Jersey, 2007.

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Forecasting

Forecasting

Forecasting can be broadly considered as a method or a technique for estimating many future aspects of a business or other operation. Planning for the future is a critical aspect of managing any organization, and small business enterprises are no exception. Indeed, their typically modest capital resources make such planning particularly important. In fact, the long-term success of both small and large organizations is closely tied to how well the management of the organization is able to foresee its future and to develop appropriate strategies to deal with likely future scenarios. Intuition, good judgment, and an awareness of how well the industry and national economy are doing may give the manager of a business firm a sense of future market and economic trends. Nevertheless, it is not easy to convert a feeling about the future into a precise and useful number, such as next year's sales volume or the raw material cost per unit of output. Forecasting methods can help estimate many such future aspects of a business operation.

The goal of forecasting is to come as close to possible to an accurate picture of the future. But, as with other forms of fortune telling, it can never be fully accurate. There are simply too many interactive variables. A change in any one of these may cause the forecasted scenario to change. For example, unexpected shocks to the economy, as occurred after the terrorist attacks of 9/11, are extremely difficult to anticipate and plan around. Such extreme situations are, happily, very rare. But there are far more subtle events that may also cause major changes in the assumptions upon which a forecast is based, things like: sharply increased material costs resulting from storms or wars, the unexpected demise or buyout of a large competitor, and/or an increase in demand due to an unexpected fashion trend shift. Despite the fact that forecasting is an imprecise art, a company must do the best it can to plan for the future and an important part of this planning is forecasting.

The task of forecasting can be approached in a number of ways and the best forecasting outcomes are usually the result of applying several forecasting methods. To supplement their judgment, forecasters rely on a variety of data sources and forecasting methods. For example, forecasting may involve the use of econometric models that can take into account the interactions between economic variables. In other cases the forecaster may employ statistical techniques for analyzing sets of historical data referred to simply as time series. Other frequently used data sources are recent consumer surveys and forecasts produced by other institutionsindustry associations, investment banks, and economists generally.

FORECASTING AND ITS PRACTICAL APPLICATIONS

In an era where forecasts drive entire supply chain networks forecasting is an increasingly critical organizational capability. Forecasting the future may sound like a lofty and theoretical activity when in reality it is a practical business tool like many others. Here is an example. How should a business go about preparing the quarterly sales volume forecasts for their primary product, say, window-glass? The company will certainly want to review the actual sales data for window glass over the last few years. Suppose that the forecaster has access to actual sales data for each quarter over the 15-year period the firm has been in business. Using these historical data, the forecaster can see the general level of sales but more importantly, he or she can also determine what pattern the sales history produces, what trends are visible. A thorough review of the data may reveal some type of seasonal pattern, such as peak sales occurring in the spring as people do spring-cleaning and others prepare to sell their homes during the summer school break. In addition, if the forecaster is able to identify other factors that influence sales, like weather patterns or housing starts, historical data on these factors can also be used in generating forecasts of future sales volumes.

FORECASTING METHODS

Academics divide forecasting methods into two broad categories: qualitative and quantitative. The division of forecasting methods into qualitative forecasting and quantitative forecasting is based on the availability of historical time series data. If historical data and time series are available, than quantitative methods may be used. If not, qualitative methods are the only option.

Qualitative Forecasting Methods

Qualitative forecasting techniques generally employ the judgment of experts to generate forecasts. A key advantage of these procedures is that they can be applied in situations where historical data are simply not available. Even in situations where such data are available, quantitative forecasting methods are a useful addition to successful forecasting. Three important qualitative forecasting methods are: the Delphi method, scenario writing, and the subject approach.

Delphi Method

In the Delphi method, an attempt is made to develop forecasts through "group consensus."

A group of experts in a particular field participate. Usually, a panel of these experienced people is asked to respond to a series of questionnaires. The panel members, who should ideally come from a variety of backgrounds (marketing, production, management, finance, purchasing, etc.) are asked to respond to an initial questionnaire. A second questionnaire is then created which incorporates information and opinions gathered in the responses to the first questionnaire. The second questionnaire is then distributed. Each panelist is asked to reconsider and revise his or her initial response to the questions based on the new information. This process is continued until some degree of consensus among the panelists is reached. It should be noted that the objective of the Delphi method is not to produce a single answer at the end. Instead, it attempts to produce a relatively narrow range of opinionsa range into which most of the panelists' opinions fall.

Scenario Writing Method

Under the scenario writing approach, the forecaster starts with different sets of assumptions. For each set of assumptions, a likely scenario of the business outcome is charted. Thus, the forecaster generates several different future scenarios (corresponding to different sets of assumptions). The decision maker or business person is presented with the different scenarios, and has to decide which scenario is most likely to prevail.

A Subjective Approach Method

The subjective approach allows individuals participating in the forecasting decision to arrive at a forecast based on their feelings, ideas, and personal experiences. Many corporations in the United States have started to increasingly use the subjective approach. Internally, these subjective approaches sometimes take the form of "brainstorming sessions," in which managers, executives, and employees work together to develop new ideas or to solve complex problems. At other times, the subjective approach may take the form of a survey of the company's sales people. This approach, which is known as the sales force composite or grass roots method, is relied on because salespeople interact directly with purchasers and it is assumed therefore that they have a good feel for which products will or will not sell and in what quantities.

The advantage of using the salespeople's forecasts is that salespeople are highly qualified to explain the demand for products, especially in their own territories. The disadvantage is that salespeople may tend to be optimistic in their estimates since optimism is a characteristic often found in good salespeople. Also, those working in sales may fear that a low sales forecast will lead to layoffs in the sales area. The opinions of salespeople should not be relied on to the exclusion of all else for one additional reason. Salespeople may not be aware of impending changes in other related areas, such as availability of raw materials, national economic developments, or the arrival of a formidable new competitor.

Quantitative Forecasting Methods

Quantitative forecasting methods are used when historical data on variables of interest are availablethese methods are based on an analysis of historical data concerning the time series of the specific variable of interest. There are two quantitative forecasting methods. The first uses the past trend of a particular variable in order to make a future forecast of the variable. In recognition of this method's reliance on time series, it is commonly called the "time series method." The second quantitative forecasting method also uses historical data. This method is often referred to as the causal method because it relies on the use of several variables and their "cause-and-effect" relationships. Examples of variables that may have this cause-and-effect relationship are: 1) interest rate levels and levels of disposable income; 2) winter weather patterns and demand for heating oil; 3) increasing gas prices and a decline in demand for sports utility vehicles (SUVs). By studying the time series data on two or more variables that have a cause-and-effect relationship with the item for which a forecast is needed, effort is made to incorporate as many relevant factors as possible into the forecast.

In practice, most business people use some combination of these methods and techniques in trying to plan for the future and put together accurate forecasts. With each cycle of forecasting, more is learned about what factor to consider and how to weight their importance in projecting future events.

see also Business Planning; Sales Forecasts

BIBLIOGRAPHY

Aston, Adam, and Joseph Weber. "The Worst Isn't Over: Smarter science is helping companies and insurers plan for hurricanes. The Bad News: This year could be another doozy." Business Week. 16 January 2006.

Chase, Charles W. Jr. "Composite Forecasting: Combining Forecasts for Improved Accuracy." Journal of Business Forecasting. Summer 2000.

Engerman, Stanley. "On the Accuracy of Some Past and Present Forecasts." International Monetary Fund Staff Papers. Annual 2005.

Evans, Michael. Practical Business Forecasting. Blackwell Publishing, 2002.

Gaber, Tal, Jacob Goldenberg, Barak Libai, and Eitan Mullerray. "From Density to Destiny: Using spatial dimension of sales data for early prediction of new product success." Marketing Science. Summer 2004.

Gray, Andi. "How Forecasting Can Help the Bottom Line." Fairfield County Business Journal. 27 June 2005.

Jones, Vernon Dale, Stuart Bretschneider, and Wilpen L. Gorr. "Organization Pressures on Forecast Evaluation: Managerial, Political, and Procedural Influences." Journal of Forecasting. July 1997.

Mentzer, John T., and Mark A. Moon. Sales Forecasting Management. Sage Publications, Inc., 2004.

O'Connor, Marcus, William Remus, and Ken Griggs. "Going UpGoing Down: How Good are People at Forecasting Trends and Changes in Trends?" Journal of Forecasting. May 1997.

Sanders, Nada R., and Karl B. Manrodt. "The Efficacy of Using Judgmental versus Quantitative Forecasting Methods in Practice." Omega. December 2003.

Rasmussen, Rasmus. "On Time Series Data and Optimal Parameters." Omega. April 2004.

                             Hillstrom, Northern Lights

                               updated by Magee, ECDI

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forecast

fore·cast / ˈfôrˌkast/ • v. (past -cast or -cast·ed) [tr.] predict or estimate (a future event or trend): rain is forecast for eastern Ohio | [tr.] coal consumption is forecast to increase. • n. a prediction or estimate of future events, esp. coming weather or a financial trend. DERIVATIVES: fore·cast·er n.

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forecast

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