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| {{Other uses|Forecast (disambiguation)}}
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| '''Forecasting''' is the process of making statements about events whose actual outcomes (typically) have not yet been observed. A commonplace example might be [[Approximation|estimation]] of some variable of interest at some specified future date. [[Prediction]] is a similar, but more general term. Both might refer to formal statistical methods employing [[time series]], [[cross-sectional data|cross-sectional]] or [[longitudinal study|longitudinal]] data, or alternatively to less formal judgemental methods. Usage can differ between areas of application: for example, in [[hydrology]], the terms "forecast" and "forecasting" are sometimes reserved for estimates of values at certain specific [[future]] times, while the term "prediction" is used for more general estimates, such as the number of times floods will occur over a long period. | |
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| [[Risk]] and [[uncertainty]] are central to forecasting and prediction; it is generally considered good practice to indicate the degree of uncertainty attaching to forecasts. In any case, the data must be up to date in order for the forecast to be as accurate as possible.<ref>{{cite web|url=http://www.forecastingprinciples.com/index.php/faq| title=Answers to Frequently Asked Questions| author=Scott Armstrong, Fred Collopy, Andreas Graefe and Kesten C. Green| accessdate=May 15, 2013}}</ref> <!-- old FAQ version here: http://qbox.wharton.upenn.edu/documents/mktg/research/FAQ.pdf -->
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| ==Categories of forecasting methods==
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| ===Qualitative vs. quantitative methods===
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| Qualitative forecasting techniques are subjective, based on the opinion and judgment of consumers, experts; they are appropriate when past data are not available.
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| They are usually applied to intermediate- or long-range decisions. Examples of qualitative forecasting methods are {{cn|date=May 2012}} informed opinion and judgment, the [[Delphi method]], [[market research]], and historical life-cycle analogy.
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| Quantitative forecasting [[mathematical model|models]] are used to forecast future data as a function of past data; they are appropriate when past data are available.
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| These methods are usually applied to short- or intermediate-range decisions. Examples of quantitative forecasting methods are{{cn|date=May 2012}} last period demand, simple and weighted N-Period [[moving average]]s, simple [[exponential smoothing]], and multiplicative seasonal indexes.
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| ===Naïve approach===
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| Naïve forecasts are the most cost-effective objective forecasting model, and provide a benchmark against which more sophisticated models can be compared. For stationary time series data, this approach says that the forecast for any period equals the historical average. For time series data that are stationary in terms of [[Unit root|first difference]]s, the naïve forecast equals the previous period's actual value.
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| ===Time series methods===
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| [[Time series]] methods use historical data as the basis of estimating future outcomes.
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| *[[Moving average]]
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| *[[Weighted moving average]]
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| *[[Kalman filtering]]
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| *[[Exponential smoothing]]
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| *[[Autoregressive moving average model|Autoregressive moving average (ARMA)]]
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| *[[Autoregressive integrated moving average|Autoregressive integrated moving average (ARIMA)]]
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| :e.g. [[Box-Jenkins]]
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| *[[Extrapolation]]
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| *[[Linear prediction]]
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| *[[Trend estimation]]
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| *[[Growth curve]]
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| ===Causal / econometric forecasting methods===
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| Some forecasting methods try to identify the underlying factors that might influence the variable that is being forecast. For example, including information about climate patterns might improve the ability of a model to predict umbrella sales. Forecasting models often take account of regular seasonal variations. In addition to climate, such variations can also be due to holidays and customs: for example, one might predict that sales of college football apparel will be higher during the football season than during the off season.<ref>{{cite book|last=Nahmias|first=Steven|title=Production and Operations Analysis|year=2009}}</ref>
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| Several informal methods used in causal forecasting do not employ strict algorithms {{clarifyme|date=December 2013}}, but instead use the judgment of the forecaster. Some forecasts take account of past relationships between variables: if one variable has, for example, been approximately linearly related to another for a long period of time, it may be appropriate to extrapolate such a relationship into the future, without necessarily understanding the reasons for the relationship.
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| Causal methods include:
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| *[[Regression analysis]] includes a large group of methods for predicting future values of a variable using information about other variables. These methods include both [[parametric statistics|parametric]] (linear or non-linear) and [[Nonparametric regression|non-parametric]] techniques.
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| *[[ARMAX|Autoregressive moving average with exogenous inputs (ARMAX)]]<ref>{{cite book|last=Ellis|first=Kimberly|title=Production Planning and Inventory Control Virginia Tech|year=2008|publisher=McGraw Hill|isbn=978-0-390-87106-0}}</ref>
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| Quantitative forecasting models are often judged against each other by comparing their in-sample or out-of-sample [[mean square error]], although some researchers have advised against this.<ref>{{cite journal|url=http://marketing.wharton.upenn.edu/ideas/pdf/armstrong2/armstrong-errormeasures-empirical.pdf | title = Error Measures For Generalizing About Forecasting Methods: Empirical Comparisons | author = J. Scott Armstrong and Fred Collopy | journal = International Journal of Forecasting | volume = 8 | pages = 69–80 | year = 1992}}</ref>
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| ===Judgmental methods===
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| Judgmental forecasting methods incorporate intuitive judgements, opinions and subjective [[probability]] estimates.
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| *[[Composite forecasts]]
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| *[[Delphi method]]
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| *[[Forecast by analogy]]
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| *[[Scenario building]]
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| *[[Statistical survey]]s
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| *[[Technology forecasting]]
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| ===Artificial intelligence methods===
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| *[[Artificial neural networks]]
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| *[[Group method of data handling]]
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| *[[Support vector machine]]s
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| Often these are done today by specialized programs loosely labeled
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| *[[Data mining]]
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| *[[Machine Learning]]
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| *[[Pattern Recognition]]
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| ===Other methods===
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| *[[Simulation]]
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| *[[Prediction market]]
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| *[[Probabilistic forecasting]] and [[Ensemble forecasting]]
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| ==Forecasting accuracy==
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| The forecast error is the difference between the actual value and the forecast value for the corresponding period.
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| <math>\ E_t = Y_t - F_t </math> | |
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| where E is the forecast error at period t, Y is the actual value at period t, and F is the forecast for period t.
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| Measures of aggregate error:
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| {| class=wikitable
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| |[[Mean absolute error]] (MAE)
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| |<math>\ MAE = \frac{\sum_{t=1}^{N} |E_t|}{N} </math>
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| |[[Mean Absolute Percentage Error]] (MAPE)
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| |<math>\ MAPE = \frac{\sum_{t=1}^N |\frac{E_t}{Y_t}|}{N} </math>
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| |Mean Absolute Deviation (MAD)
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| |<math>\ MAD = \frac{\sum_{t=1}^{N} |E_t|}{N} </math>
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| |Percent Mean Absolute Deviation (PMAD)
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| |<math>\ PMAD = \frac{\sum_{t=1}^{N} |E_t|}{\sum_{t=1}^{N} |Y_t|} </math>
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| |[[Mean squared error]] (MSE) or [[Mean squared prediction error]] (MSPE)
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| |<math>\ MSE = \frac{\sum_{t=1}^N {E_t^2}}{N} </math>
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| |Root Mean squared error (RMSE)
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| |<math>\ RMSE = \sqrt{\frac{\sum_{t=1}^N {E_t^2}}{N}} </math>
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| |[[Forecast skill]] (SS)
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| |<math>\ SS = 1- \frac{MSE_{forecast}}{MSE_{ref}} </math>
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| |Average of Errors (E)
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| |<math>\ \bar{E}= \frac{\sum_{i=1}^N {E_i}}{N} </math>
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| |}
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| Business forecasters and practitioners sometimes use different terminology in the industry. They refer to the PMAD as the MAPE, although they compute this as a volume weighted MAPE.{{cn|date=May 2012}} For more information see [[Calculating demand forecast accuracy]].
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| '''See also''' | |
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| *[[Calculating demand forecast accuracy]]
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| *[[Consensus forecasts]]
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| *[[Forecast error]]
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| *[[Predictability]]
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| *[[Prediction interval]]s, similar to [[confidence interval]]s
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| *[[Reference class forecasting]]
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| ==Applications of forecasting==
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| Climate change and increasing energy prices have led to the use of [[Egain Forecasting]] for buildings. This attempts to reduce the energy needed to heat the building, thus reducing the emission of greenhouse gases. Forecasting is used in [[Customer Demand Planning]] in everyday business for manufacturing and distribution companies.
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| Forecasting has also been used to predict the development of conflict situations. Forecasters perform research that uses empirical results to gauge the effectiveness of certain forecasting models.<ref>{{cite web|url=http://qbox.wharton.upenn.edu/documents/mktg/research/FAQ.pdf | title = Answers to Frequently Asked Questions | author = J. Scott Armstrong, Kesten C. Green and Andreas Graefe | year = 2010}}</ref> However research has shown that there is little difference between the accuracy of the forecasts of experts knowledgeable in the conflict situation and those by individuals who knew much less.<ref>{{cite journal|url=http://marketing.wharton.upenn.edu/documents/research/Value%20of%20expertise.pdf | title = The Ombudsman: Value of Expertise for Forecasting Decisions in Conflicts | author = Kesten C. Greene and J. Scott Armstrong | journal = Interfaces | volume = 0 | pages = 1–12 | year = 2007 | publisher = INFORMS}}</ref>
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| Similarly, experts in some studies argue that role thinking{{clarifyme|date=December 2013}} does not contribute to the accuracy of the forecast.<ref>{{cite journal|url= http://www.forecastingprinciples.com/paperpdf/Escalation%20Bias.pdf | title = Role thinking: Standing in other people’s shoes to forecast decisions in conflicts | author = Kesten C. Green and J. Scott Armstrong| journal = Role thinking: Standing in other people’s shoes to forecast decisions in conflicts | volume = 39 | pages = 111–116 | year = 1975}}</ref> The discipline of demand planning, also sometimes referred to as supply chain forecasting, embraces both statistical forecasting and a consensus process. An important, albeit often ignored aspect of forecasting, is the relationship it holds with [[planning]]. Forecasting can be described as predicting what the future ''will'' look like, whereas planning predicts what the future ''should'' look like.<ref>{{cite web|url=http://www.forecastingprinciples.com/index.php?option=com_content&task=view&id=3&Itemid=3 |title=FAQ |publisher=Forecastingprinciples.com |date=1998-02-14 |accessdate=2012-08-28}}</ref><ref>
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| {{cite web|url=http://www.qbox.wharton.upenn.edu/documents/mktg/research/INTFOR3581%20-%20Publication%
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| 2015.pdf |format=PDF | title = Structured analogies for forecasting | author = Kesten C. Greene and J. Scott Armstrong |publisher = qbox.wharton.upenn.edu}}</ref> There is no single right forecasting method to use. Selection of a method should be based on your objectives and your conditions (data etc.).<ref>{{cite web|url=http://www.forecastingprinciples.com/index.php?option=com_content&task=view&id=3&Itemid=3#D._Choosing_the_best_method |title=FAQ |publisher=Forecastingprinciples.com |date=1998-02-14 |accessdate=2012-08-28}}</ref> A good place to find a method, is by visiting a selection tree. An example of a selection tree can be found here.<ref>{{cite web|url=http://www.forecastingprinciples.com/index.php?option=com_content&task=view&id=17&Itemid=17 |title=Selection Tree |publisher=Forecastingprinciples.com |date=1998-02-14 |accessdate=2012-08-28}}</ref>
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| Forecasting has application in many situations:
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| *[[Supply chain management]] - Forecasting can be used in supply chain management to ensure that the right product is at the right place at the right time. Accurate forecasting will help retailers reduce excess inventory and thus increase profit margin. Studies have shown that extrapolations are the least accurate, while company earnings forecasts are the most reliable.{{clarifyme|date=December 2013}}<ref>{{cite journal|url=http://www.forecastingprinciples.com/paperpdf/Monetary%20Incentives.pdf | title = Relative Accuracy of Judgmental and Extrapolative Methods in Forecasting Annual Earnings | author = J. Scott Armstrong| journal = Journal of Forecasting | volume = 2 | pages = 437–447 | year = 1983}}</ref> Accurate forecasting will also help them meet consumer demand.
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| *[[Economic forecasting]]
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| *[[Earthquake prediction]]
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| *[[Egain forecasting]]
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| *[[Land use forecasting]]
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| *[[PECOTA|Player and team performance in sports]]
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| *[[Political forecasting]]
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| *[[Product forecasting]]
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| *[[Sales forecasting]]
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| *[[Technology forecasting]]
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| *[[Telecommunications forecasting]]
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| *[[Transport planning]] and [[Transportation forecasting]]
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| *[[Weather forecasting]], [[Flood forecasting]] and [[Meteorology]]
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| ==Limitations==
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| Limitations pose barriers beyond which forecasting methods cannot reliably predict.
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| === Performance limits of fluid dynamics equations ===
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| As proposed by [[Edward Lorenz]] in 1963, long range weather forecasts, those made at a range of two weeks or more, are impossible to definitively predict the state of the atmosphere, owing to the [[chaos theory|chaotic nature]] of the [[fluid dynamics]] equations involved. Extremely small errors in the initial input, such as temperatures and winds, within numerical models double every five days.<ref>{{cite book|title=Storm Watchers|pages=222–224|year=2002|author=Cox, John D.|publisher=John Wiley & Sons, Inc.|isbn=0-471-38108-X}}</ref>
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| === Complexity introduced by the technological singularity ===
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| {{Main|Technological singularity}}
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| The [[technological singularity]] is the theoretical emergence of [[superintelligence]] through technological means.<ref>Superintelligence. Answer to the 2009 EDGE QUESTION: "WHAT WILL CHANGE EVERYTHING?": http://www.nickbostrom.com/views/superintelligence.pdf</ref> Since the capabilities of such intelligence would be difficult for an unaided human mind to comprehend, the technological singularity is seen as an occurrence beyond which events cannot be predicted.
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| [[Ray Kurzweil]] predicts the singularity will occur around 2045 while [[Vernor Vinge]] predicts it will happen some time before 2030.
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| ==See also==
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| <div style="-moz-column-count:2; column-count:2;">
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| * [[Collaborative planning, forecasting, and replenishment|CPFR]]
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| * [[Forecasting bias]]
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| * [[Foresight (future studies)]]
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| * [[Futures studies]]
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| * [[Futurology]]
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| * [[Optimism bias]]
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| * [[Planning]]
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| * [[Strategic foresight]]
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| * [[Technology forecasting]]
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| * [[Wind power forecasting]]
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| * [[Earthquake prediction]]
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| * [[Weather forecasting]]
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| * [[Time Series]]
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| </div>
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| ==References==
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| {{Reflist}}
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| *{{cite book
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| |author = [[Armstrong, J. Scott]] (ed.)
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| |title= ''Principles of forecasting: a handbook for researchers and practitioners
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| |year= 2001
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| |publisher= Kluwer Academic Publishers
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| |location= Norwell, Massachusetts
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| |language= [[English language|English]]
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| |isbn= 0-7923-7930-6
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| }}
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| *{{cite book
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| | author=Ellis, Kimberly
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| | title = Production Planning and Inventory Control
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| | year = 2010
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| | publisher = McGraw-Hill
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| | language = [[English language|English]]
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| | isbn = 0-412-03471-9
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| }}
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| *{{cite book
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| | author=Geisser, Seymour
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| | authorlink =Seymour Geisser
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| | title = Predictive Inference: An Introduction
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| | date = 1 June 1993
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| | publisher = Chapman & Hall, CRC Press
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| | language = [[English language|English]]
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| | isbn = 0-390-87106-0
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| }}
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| *{{cite book
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| | author=Gilchrist, Warren
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| | title = Statistical Forecasting
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| | year = 1976
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| | publisher = John Wiley & Sons
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| | location = London
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| | language = [[English language|English]]
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| | isbn = 0-471-99403-0
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| }}
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| *Hyndman, R.J., Koehler, A.B (2005) [http://www.robjhyndman.com/papers/mase.pdf "Another look at measures of forecast accuracy"], Monash University note.
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| *{{cite book
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| | author=Makridakis, Spyros
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| | coauthors=Wheelwright, Steven; [[Hyndman, Rob J.]]
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| | title= Forecasting: methods and applications
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| | url= http://www.robjhyndman.com/forecasting/
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| | year=1998
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| | publisher = John Wiley & Sons
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| | location = New York
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| | language = [[English language|English]]
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| | isbn= 0-471-53233-9
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| }}
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| *{{cite book
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| |author = Kress, George J.
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| |coauthors= Snyder, John
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| |title= ''Forecasting and market analysis techniques: a practical approach
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| |date= 30 May 1994
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| |publisher= Quorum Books
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| |location= Westport, Connecticut, London
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| |language= [[English language|English]]
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| |isbn= 0-89930-835-X
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| }}
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| *{{cite book
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| | author=Rescher, Nicholas
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| | authorlink =Nicholas Rescher
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| | title = Predicting the future: An introduction to the theory of forecasting
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| | year = 1998
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| | publisher = State University of New York Press
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| | language = [[English language|English]]
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| | isbn = 0-7914-3553-9
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| }}
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| *Sasic Kaligasidis, A et al. (2006) Upgraded weather forecast control of building heating systems. p. 951 ff in Research in Building Physics and Building Engineering Paul Fazio (Editorial Staff), ISBN 0-415-41675-2
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| *Taesler, R. (1990/91) Climate and Building Energy Management. Energy and Buildings, Vol. 15-16, pp 599 – 608.
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| *[[Peter Turchin|Turchin, P.]] (2007) "Scientific Prediction in Historical Sociology: Ibn Khaldun meets Al Saud". In:[http://edurss.ru/cgi-bin/db.pl?cp=&page=Book&id=53185&lang=en&blang=en&list=Found ''History & Mathematics: Historical Dynamics and Development of Complex Societies.''] Moscow: KomKniga. ISBN 978-5-484-01002-8
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| *United States Patent 6098893 Comfort control system incorporating weather forecast data and a method for operating such a system (Inventor Stefan Berglund)
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| ==External links==
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| {{wiktionary|predict}}
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| {{wiktionary|forecast}}
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| *[http://www.forecastingprinciples.com Forecasting Principles: ''"Evidence-based forecasting"'']
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| *[http://www.forecasters.org International Institute of Forecasters]
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| *[http://www.itl.nist.gov/div898/handbook/pmc/section4/pmc4.htm Introduction to Time series Analysis (Engineering Statistics Handbook)] - A practical guide to Time series analysis and forecasting
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| *[http://www.statsoft.com/textbook/sttimser.html Time Series Analysis]
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| *[http://www.ifs.du.edu Global Forecasting with IFs]
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| *[http://www.quakefinder.com Earthquake Electromagnetic Precursor Research]
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| [[Category:Data analysis]]
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| [[Category:Statistical forecasting]]
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| [[Category:Time series analysis]]
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| [[Category:Supply chain management terms]]
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| [[Category:Supply chain analytics]]
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| [[bg:Предвиждане на бъдещи събития]]
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| [[eu:Aurresan]]
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| [[fr:Prévision]]
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| [[hi:भविष्यवाणी]]
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| [[ru:Предсказание]]
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| [[simple:Forecasting]]
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