Forecasting
Encyclopedia
Forecasting is the process of making statements about events whose actual outcomes (typically) have not yet been observed. A commonplace example might be estimation
for 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
, crosssectional
or 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. Risk
and uncertainty
are central to forecasting and prediction; it is generally considered good practice to indicate the degree of uncertainty attaching to forecasts.
The process of climate change and increasing energy prices has led to the usage of Egain Forecasting
of buildings. The method uses Forecasting to reduce the energy needed to heat the building, thus reducing the emission of greenhouse gases.
Forecasting is used in the practice of Customer Demand Planning
in every day business forecasting for manufacturing companies. 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. There is no single right forecasting method to use. Selection of a method should be based on your objectives and your conditions (data etc.). A good place to find a method, is by visiting a selection tree. An example of a selection tree can be found here.
It is usually applied to intermediatelong range decisions.
Example of qualitative forecasting methods:
Quantitative forecasting models are used to estimate future demands as a function of past data; appropriate when past data is available.
It is usually applied to shortintermediate range decisions.
Example of Quantitative forecasting methods:
methods use historical data as the basis of estimating future outcomes.
Casual forecasting methods are also subject to the discretion of the forecaster. There are several informal methods which do not have strict algorithms, but rather modest and unstructured guidance. One can forecast based on, for example, linear relationships. If one variable is linearly related to the other for a long enough period of time, it may be beneficial to predict such a relationship in the future. This is quite different from the aforementioned model of seasonality whose graph would more closely resemble a sine or cosine wave. The most important factor when performing this operation is using concrete and substantiated data. Forecasting off of another forecast produces inconclusive and possibly erroneous results.
Such methods include:
estimates.
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.
Measures of aggregate error:
{N}

Mean Absolute Percentage Error
(MAPE)


Mean Absolute Deviation (MAD)


Percent Mean Absolute Deviation (PMAD)


Mean squared error
(MSE)


Root Mean squared error (RMSE)


Forecast skill
(SS)


Average of Errors (E)

}
Please note that business forecasters and practitioners sometimes use different terminology in the industry. They refer to the PMAD as the MAPE, although they compute this volume weighted MAPE. For more information see Calculating Demand Forecast Accuracy
Reference class forecasting
was developed to increase forecasting accuracy.
See also
Estimation
Estimation is the calculated approximation of a result which is usable even if input data may be incomplete or uncertain.In statistics,*estimation theory and estimator, for topics involving inferences about probability distributions...
for some variable of interest at some specified future date. Prediction
Prediction
A prediction or forecast is a statement about the way things will happen in the future, often but not always based on experience or knowledge...
is a similar, but more general term. Both might refer to formal statistical methods employing time series
Time series
In statistics, signal processing, econometrics and mathematical finance, a time series is a sequence of data points, measured typically at successive times spaced at uniform time intervals. Examples of time series are the daily closing value of the Dow Jones index or the annual flow volume of the...
, crosssectional
Crosssectional data
Crosssectional data or cross section in statistics and econometrics is a type of onedimensional data set. Crosssectional data refers to data collected by observing many subjects at the same point of time, or without regard to differences in time...
or longitudinal
Longitudinal study
A longitudinal study is a correlational research study that involves repeated observations of the same variables over long periods of time — often many decades. It is a type of observational study. Longitudinal studies are often used in psychology to study developmental trends across the...
data, or alternatively to less formal judgemental methods. Usage can differ between areas of application: for example in hydrology
Hydrology
Hydrology is the study of the movement, distribution, and quality of water on Earth and other planets, including the hydrologic cycle, water resources and environmental watershed sustainability...
, the terms "forecast" and "forecasting" are sometimes reserved for estimates of values at certain specific future
Future
The future is the indefinite time period after the present. Its arrival is considered inevitable due to the existence of time and the laws of physics. Due to the nature of the reality and the unavoidability of the future, everything that currently exists and will exist is temporary and will come...
times, while the term "prediction" is used for more general estimates, such as the number of times floods will occur over a long period. Risk
Risk
Risk is the potential that a chosen action or activity will lead to a loss . The notion implies that a choice having an influence on the outcome exists . Potential losses themselves may also be called "risks"...
and uncertainty
Uncertainty
Uncertainty is a term used in subtly different ways in a number of fields, including physics, philosophy, statistics, economics, finance, insurance, psychology, sociology, engineering, and information science...
are central to forecasting and prediction; it is generally considered good practice to indicate the degree of uncertainty attaching to forecasts.
The process of climate change and increasing energy prices has led to the usage of Egain Forecasting
Egain Forecasting
Egain forecasting is a method of controlling building heating by calculating demand for heating energy that should be supplied to the building in each time unit. By combining physics of structures with meteorology, properties of the building, weather conditions including outdoor temperature, wind...
of buildings. The method uses Forecasting to reduce the energy needed to heat the building, thus reducing the emission of greenhouse gases.
Forecasting is used in the practice of Customer Demand Planning
Customer Demand Planning
Customer Demand Planning is a businessplanning process, that enables sales teams to develop demand forecasts as input to serviceplanning processes, production, inventory planning and revenue planning. Definition of CDP :...
in every day business forecasting for manufacturing companies. 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
Planning
Planning in organizations and public policy is both the organizational process of creating and maintaining a plan; and the psychological process of thinking about the activities required to create a desired goal on some scale. As such, it is a fundamental property of intelligent behavior...
. Forecasting can be described as predicting what the future will look like, whereas planning predicts what the future should look like. There is no single right forecasting method to use. Selection of a method should be based on your objectives and your conditions (data etc.). A good place to find a method, is by visiting a selection tree. An example of a selection tree can be found here.
Qualitative vs. Quantitative Methods
Qualitative forecasting techniques are subjective, based on the opinion and judgment of consumers, experts; appropriate when past data is not available.It is usually applied to intermediatelong range decisions.
Example of qualitative forecasting methods:
 Informed opinion and judgment
 Delphi method
 Market research
 Historical lifecycle Analogy.
Quantitative forecasting models are used to estimate future demands as a function of past data; appropriate when past data is available.
It is usually applied to shortintermediate range decisions.
Example of Quantitative forecasting methods:
 Last period demand
 Arithmetic Average
 Simple Moving Average (NPeriod)
 Weighted Moving Average (Nperiod)
 Simple Exponential Smoothing
 Multiplicative Seasonal Indexes
Naïve Approach
Naïve forecasts are the most costeffective and efficient objective forecasting model, and provide a benchmark against which more sophisticated models can be compared. For stable time series data, this approach says that the forecast for any period equals the previous period's actual value.Time series methods
Time seriesTime series
In statistics, signal processing, econometrics and mathematical finance, a time series is a sequence of data points, measured typically at successive times spaced at uniform time intervals. Examples of time series are the daily closing value of the Dow Jones index or the annual flow volume of the...
methods use historical data as the basis of estimating future outcomes.
 Moving average
 Weighted moving average
 Exponential smoothingExponential smoothingExponential smoothing is a technique that can be applied to time series data, either to produce smoothed data for presentation, or to make forecasts. The time series data themselves are a sequence of observations. The observed phenomenon may be an essentially random process, or it may be an...
 Autoregressive moving average (ARMA)Autoregressive moving average modelIn statistics and signal processing, autoregressive–movingaverage models, sometimes called Box–Jenkins models after the iterative Box–Jenkins methodology usually used to estimate them, are typically applied to autocorrelated time series data.Given a time series of data Xt, the ARMA model is a...
 Autoregressive integrated moving average (ARIMA)Autoregressive integrated moving averageIn statistics and econometrics, and in particular in time series analysis, an autoregressive integrated moving average model is a generalization of an autoregressive moving average model. These models are fitted to time series data either to better understand the data or to predict future points...
 e.g. BoxJenkinsBoxJenkinsIn time series analysis, the Box–Jenkins methodology, named after the statisticians George Box and Gwilym Jenkins, applies autoregressive moving average ARMA or ARIMA models to find the best fit of a time series to past values of this time series, in order to make forecasts.Modeling approach:The...
 ExtrapolationExtrapolationIn mathematics, extrapolation is the process of constructing new data points. It is similar to the process of interpolation, which constructs new points between known points, but the results of extrapolations are often less meaningful, and are subject to greater uncertainty. It may also mean...
 Linear predictionLinear predictionLinear prediction is a mathematical operation where future values of a discretetime signal are estimated as a linear function of previous samples....
 Trend estimationTrend estimationTrend estimation is a statistical technique to aid interpretation of data. When a series of measurements of a process are treated as a time series, trend estimation can be used to make and justify statements about tendencies in the data...
 Growth curveGrowth curveA growth curve is an empirical model of the evolution of a quantity over time. Growth curves are widely used in biology for quantities such as population size, body height or biomass...
 Extrapolation
Causal / econometric forecasting methods
Some forecasting methods use the assumption that it is possible to identify the underlying factors that might influence the variable that is being forecast. For example, including information about weather conditions might improve the ability of a model to predict umbrella sales. This is a model of seasonality which shows a regular pattern of up and down fluctuations. In addition to weather, seasonality can also be due to holidays and customs such as predicting that sales in college football apparel will be higher during football season as opposed to the off season.Casual forecasting methods are also subject to the discretion of the forecaster. There are several informal methods which do not have strict algorithms, but rather modest and unstructured guidance. One can forecast based on, for example, linear relationships. If one variable is linearly related to the other for a long enough period of time, it may be beneficial to predict such a relationship in the future. This is quite different from the aforementioned model of seasonality whose graph would more closely resemble a sine or cosine wave. The most important factor when performing this operation is using concrete and substantiated data. Forecasting off of another forecast produces inconclusive and possibly erroneous results.
Such methods include:
 Regression analysisRegression analysisIn statistics, regression analysis includes many techniques for modeling and analyzing several variables, when the focus is on the relationship between a dependent variable and one or more independent variables...
includes a large group of methods that can be used to predict future values of a variable using information about other variables. These methods include both parametricParametricParametric may refer to:*Parametric equation*Parametric statistics*Parametric derivative*Parametric plot*Parametric model*Parametric oscillator *Parametric contract*Parametric insurance*Parametric feature based modeler...
(linear or nonlinear) and nonparametric techniques.
 Autoregressive moving average with exogenous inputs (ARMAX)
Judgmental methods
Judgmental forecasting methods incorporate intuitive judgements, opinions and subjective probabilityProbability
Probability is ordinarily used to describe an attitude of mind towards some proposition of whose truth we arenot certain. The proposition of interest is usually of the form "Will a specific event occur?" The attitude of mind is of the form "How certain are we that the event will occur?" The...
estimates.
 Composite forecasts
 SurveysStatistical surveySurvey methodology is the field that studies surveys, that is, the sample of individuals from a population with a view towards making statistical inferences about the population using the sample. Polls about public opinion, such as political beliefs, are reported in the news media in democracies....
 Delphi methodDelphi methodThe Delphi method is a structured communication technique, originally developed as a systematic, interactive forecasting method which relies on a panel of experts.In the standard version, the experts answer questionnaires in two or more rounds...
 Scenario building
 Technology forecastingTechnology forecastingTechnology forecasting attempts to predict the future characteristics of useful technological machines, procedures or techniques.Important aspects:...
 Forecast by analogyForecast by analogyForecast by analogy is a forecasting method that assumes that two different kinds of phenomena share the same model of behaviour. For example, one way to predict the sales of a new product is to choose an existing product which "looks like" the new product in terms of the expected demand pattern...
Artificial intelligence methods
 Artificial neural networks
 Group method of data handlingGroup method of data handlingGroup method of data handling is a family of inductive algorithms for computerbased mathematical modeling of multiparametric datasets that features fully automatic structural and parametric optimization of models....
 Support vector machines
Other methods
 SimulationSimulationSimulation is the imitation of some real thing available, state of affairs, or process. The act of simulating something generally entails representing certain key characteristics or behaviours of a selected physical or abstract system....
 Prediction marketPrediction marketPrediction markets are speculative markets created for the purpose of making predictions...
 Probabilistic forecastingProbabilistic forecastingProbabilistic forecasting summarises what is known, or opinions about, future events. In contrast to a singlevalued forecasts , probabilistic forecasts assign a probability to each of a number of different outcomes,...
and Ensemble forecastingEnsemble forecastingEnsemble forecasting is a numerical prediction method that is used to attempt to generate a representative sample of the possible future states of a dynamical system...  Reference class forecastingReference class forecastingReference class forecasting is the method of predicting the future, through looking at similar past situations and their outcomes.Reference class forcasting predicts the outcome of a planned action based on actual outcomes in a reference class of similar actions to that being forecast. The theories...
Forecasting accuracy
The forecast error is the difference between the actual value and the forecast value for the corresponding period.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.
Measures of aggregate error:
Mean absolute error Mean absolute error In statistics, the mean absolute error is a quantity used to measure how close forecasts or predictions are to the eventual outcomes. The mean absolute error is given by... (MAE) 

Mean Absolute Percentage Error
Mean Absolute Percentage Error
Mean absolute percentage error is measure of accuracy in a fitted time series value in statistics, specifically trending. It usually expresses accuracy as a percentage, and is defined by the formula:...
(MAPE)


Mean Absolute Deviation (MAD)


Percent Mean Absolute Deviation (PMAD)


Mean squared error
Mean squared error
In statistics, the mean squared error of an estimator is one of many ways to quantify the difference between values implied by a kernel density estimator and the true values of the quantity being estimated. MSE is a risk function, corresponding to the expected value of the squared error loss or...
(MSE)


Root Mean squared error (RMSE)


Forecast skill
Forecast skill
Skill in forecasting is a scaled representation of forecast error that relates the forecast accuracy of a particular forecast model to some reference model....
(SS)


Average of Errors (E)

}
Please note that business forecasters and practitioners sometimes use different terminology in the industry. They refer to the PMAD as the MAPE, although they compute this volume weighted MAPE. For more information see Calculating Demand Forecast Accuracy
Calculating Demand Forecast Accuracy
Calculating demand forecast accuracy is the process of determining the accuracy of forecasts made regarding customer demand for a product.Importance of forecasts:...
Reference class forecasting
Reference class forecasting
Reference class forecasting is the method of predicting the future, through looking at similar past situations and their outcomes.Reference class forcasting predicts the outcome of a planned action based on actual outcomes in a reference class of similar actions to that being forecast. The theories...
was developed to increase forecasting accuracy.
See also
 Forecast errorForecast errorIn statistics, a forecast error is the difference between the actual or real and the predicted or forecast value of a time series or any other phenomenon of interest....
 Calculating Demand Forecast AccuracyCalculating Demand Forecast AccuracyCalculating demand forecast accuracy is the process of determining the accuracy of forecasts made regarding customer demand for a product.Importance of forecasts:...
 Consensus forecastsConsensus forecastsIn a number of sciences, ranging from econometrics to meteorology, consensus forecasts are predictions of the future that are created by combining together several separate forecasts which have often been created using different methodologies...
 PredictabilityPredictabilityPredictability is the degree to which a correct prediction or forecast of a system's state can be made either qualitatively or quantitatively.Predictability and Causality:...
 Prediction intervalPrediction intervalIn statistical inference, specifically predictive inference, a prediction interval is an estimate of an interval in which future observations will fall, with a certain probability, given what has already been observed...
, similar to confidence intervalConfidence intervalIn statistics, a confidence interval is a particular kind of interval estimate of a population parameter and is used to indicate the reliability of an estimate. It is an observed interval , in principle different from sample to sample, that frequently includes the parameter of interest, if the...
Applications of forecasting
Forecasting has application in many situations: Supply chain managementSupply chain managementSupply chain management is the management of a network of interconnected businesses involved in the ultimate provision of product and service packages required by end customers...
 Forecasting can be used in Supply Chain Management to make sure that the right product is at the right place at the right time. Accurate forecasting will help retailers reduce excess inventory and therefore increase profit margin. Accurate forecasting will also help them meet consumer demand.  Weather forecastingWeather forecastingWeather forecasting is the application of science and technology to predict the state of the atmosphere for a given location. Human beings have attempted to predict the weather informally for millennia, and formally since the nineteenth century...
, Flood forecastingFlood forecastingFlood forecasting is the use of realtime precipitation and streamflow data in rainfallrunoff and streamflow routing models to forecast flow rates and water levels for periods ranging from a few hours to days ahead, depending on the size of the watershed or river basin. Flood forecasting can also...
and MeteorologyMeteorologyMeteorology is the interdisciplinary scientific study of the atmosphere. Studies in the field stretch back millennia, though significant progress in meteorology did not occur until the 18th century. The 19th century saw breakthroughs occur after observing networks developed across several countries...  Transport planning and Transportation forecastingTransportation forecastingTransportation forecasting is the process of estimating the number of vehicles or people that will use a specific transportation facility in the future. For instance, a forecast may estimate the number of vehicles on a planned road or bridge, the ridership on a railway line, the number of...
 Economic forecastingEconomic forecastingEconomic forecasting is the process of making predictions about the economy. Forecasts can be carried out at a high level of aggregation  for example for GDP, inflation, unemployment or the fiscal deficit  or at a more disaggregated level, for specific sectors of the economy or even specific...
 Egain ForecastingEgain ForecastingEgain forecasting is a method of controlling building heating by calculating demand for heating energy that should be supplied to the building in each time unit. By combining physics of structures with meteorology, properties of the building, weather conditions including outdoor temperature, wind...
 Technology forecastingTechnology forecastingTechnology forecasting attempts to predict the future characteristics of useful technological machines, procedures or techniques.Important aspects:...
 Earthquake predictionEarthquake predictionAn earthquake prediction is a prediction that an earthquake of a specific magnitude will occur in a particular place at a particular time . Despite considerable research efforts by seismologists, scientifically reproducible predictions cannot yet be made to a specific day or month...
 Land use forecastingLand use forecastingLanduse forecasting undertakes to project the distribution and intensity of trip generating activities in the urban area. In practice, landuse models are demanddriven, using as inputs the aggregate information on growth produced by an aggregate economic forecasting activity...
 Product forecastingProduct forecastingProduct forecasting is the science of predicting the degree of success a new product will enjoy in the marketplace. To do this, the forecasting model must take into account such things as product awareness, distribution, price, fulfilling unmeet needs and competitive alternatives.Bass model:Bass...
 Player and team performance in sportsPECOTAPECOTA, an acronym for Player Empirical Comparison and Optimization Test Algorithm, is a sabermetric system for forecasting Major League Baseball player performance. The word is a backronym based on the name of journeyman major league player Bill Pecota, who with a lifetime batting average of .249...
 Telecommunications forecastingTelecommunications forecastingAll telecommunications service providers perform forecasting calculations to assist them in planning their networks. Accurate forecasting helps operators to make key investment decisions relating to product development and introduction, advertising, pricing etc., well in advance of product launch,...
 Political ForecastingPolitical forecastingPolitical forecasting aims at predicting the outcome of elections. Models include: Opinion polls :Polls are an integral part of political forecasting. However, incorporating poll results into political forecasting models can cause problems in predicting the outcome of elections...
 Sales Forecasting
External links
 Forecasting Principles: "Evidencebased forecasting"
 Introduction to Time series Analysis (Engineering Statistics Handbook)  A practical guide to Time series analysis and forecasting
 Time Series Analysis
 Global Forecasting with IFs
 Earthquake Electromagnetic Precursor Research