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Forecasting is the process of making predictions based on past and present data. Later these can be compared (resolved) against what happens. For example, a company might
estimate Estimation (or estimating) is the process of finding an estimate or approximation, which is a value that is usable for some purpose even if input data may be incomplete, uncertain, or unstable. The value is nonetheless usable because it is de ...
their revenue in the next year, then compare it against the actual results.
Prediction A prediction (Latin ''præ-'', "before," and ''dicere'', "to say"), or forecast, is a statement about a future event or data. They are often, but not always, based upon experience or knowledge. There is no universal agreement about the exact ...
is a similar but more general term. Forecasting might refer to specific formal statistical methods employing
time series In mathematics, a time series is a series of data points indexed (or listed or graphed) in time order. Most commonly, a time series is a sequence taken at successive equally spaced points in time. Thus it is a sequence of discrete-time data. Ex ...
,
cross-sectional Cross-sectional data, or a cross section of a study population, in statistics and econometrics, is a type of data collected by observing many subjects (such as individuals, firms, countries, or regions) at the one point or period of time. The analy ...
or
longitudinal Longitudinal is a geometric term of location which may refer to: * Longitude ** Line of longitude, also called a meridian * Longitudinal engine, an internal combustion engine in which the crankshaft is oriented along the long axis of the vehicle, ...
data, or alternatively to less formal judgmental methods or the process of prediction and resolution itself. Usage can vary between areas of application: for example, in
hydrology Hydrology () is the scientific study of the movement, distribution, and management of water on Earth and other planets, including the water cycle, water resources, and environmental watershed sustainability. A practitioner of hydrology is call ...
the terms "forecast" and "forecasting" are sometimes reserved for estimates of values at certain specific
future The future is the time after the past and present. Its arrival is considered inevitable due to the existence of time and the laws of physics. Due to the apparent nature of reality and the unavoidability of the future, everything that current ...
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 In simple terms, risk is the possibility of something bad happening. Risk involves uncertainty about the effects/implications of an activity with respect to something that humans value (such as health, well-being, wealth, property or the environm ...
and
uncertainty Uncertainty refers to epistemic situations involving imperfect or unknown information. It applies to predictions of future events, to physical measurements that are already made, or to the unknown. Uncertainty arises in partially observable ...
are central to forecasting and prediction; it is generally considered a 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. In some cases the data used to predict the variable of interest is itself forecast.


Applications

Forecasting has applications in a wide range of fields where estimates of future conditions are useful. Depending on the field, accuracy varies significantly. If the factors that relate to what is being forecast are known and well understood and there is a significant amount of data that can be used, it is likely the final value will be close to the forecast. If this is not the case or if the actual outcome is affected by the forecasts, the reliability of the forecasts can be significantly lower. 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 gas A greenhouse gas (GHG or GhG) is a gas that absorbs and emits radiant energy within the thermal infrared range, causing the greenhouse effect. The primary greenhouse gases in Earth's atmosphere are water vapor (), carbon dioxide (), methane ...
es. Forecasting is used in
customer demand planning Customer demand planning (CDP) is a business-planning process that enables sales teams to develop demand forecasts as input to service-planning processes, production, inventory planning and revenue planning. Definition CDP is an aspect of mana ...
in everyday business for manufacturing and distribution companies. While the veracity of predictions for actual stock returns are disputed through reference to the
efficient-market hypothesis The efficient-market hypothesis (EMH) is a hypothesis in financial economics that states that asset prices reflect all available information. A direct implication is that it is impossible to "beat the market" consistently on a risk-adjusted bas ...
, forecasting of broad economic trends is common. Such analysis is provided by both non-profit groups as well as by for-profit private institutions. Forecasting foreign exchange movements is typically achieved through a combination of chart and fundamental analysis. An essential difference between chart analysis and fundamental economic analysis is that chartists study only the price action of a market, whereas fundamentalists attempt to look to the reasons behind the action. Financial institutions assimilate the evidence provided by their fundamental and chartist researchers into one note to provide a final projection on the currency in question.Pound Sterling Live
"Euro Forecast from Institutional Researchers"
A list of collated exchange rate forecasts encompassing technical and fundamental analysis in the foreign exchange market.
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. 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. Similarly, experts in some studies argue that role thinking - standing in other people's shoes to forecast their decisions - does not contribute to the accuracy of the forecast. An important, albeit often ignored aspect of forecasting, is the relationship it holds with
planning Planning is the process of thinking regarding the activities required to achieve a desired goal. Planning is based on foresight, the fundamental capacity for mental time travel. The evolution of forethought, the capacity to think ahead, is c ...
. 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. Forecasting has application in many situations: *
Supply chain management In commerce, supply chain management (SCM) is the management of the flow of goods and services including all processes that transform raw materials into final products between businesses and locations. This can include the movement and st ...
and
customer demand planning Customer demand planning (CDP) is a business-planning process that enables sales teams to develop demand forecasts as input to service-planning processes, production, inventory planning and revenue planning. Definition CDP is an aspect of mana ...
- 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. Accurate forecasting will also help them meet consumer demand. The discipline of demand planning, also sometimes referred to as supply chain forecasting, embraces both statistical forecasting and a consensus process. Studies have shown that extrapolations are the least accurate, while company earnings forecasts are the most reliable. *
Economic forecasting Economic 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 ...
*
Earthquake prediction Earthquake prediction is a branch of the science of seismology concerned with the specification of the time, location, and magnitude of future earthquakes within stated limits, and particularly "the determination of parameters for the ''next'' ...
* Egain forecasting * Energy forecasting for renewable power integration *
Finance Finance is the study and discipline of money, currency and capital assets. It is related to, but not synonymous with economics, the study of production, distribution, and consumption of money, assets, goods and services (the discipline of f ...
against risk of default via credit ratings and
credit score A credit score is a numerical expression based on a level analysis of a person's credit files, to represent the creditworthiness of an individual. A credit score is primarily based on a credit report, information typically sourced from credit b ...
s * Land use forecasting * Player and team performance in sports * Political forecasting * Product forecasting * Sales forecasting * Technology forecasting *
Telecommunications forecasting All telecommunications service providers perform forecasting calculations to assist them in planning their networks.Farr R.E., Telecommunications Traffic, Tariffs and Costs – An Introduction For Managers, Peter Peregrinus, 1988. Accurate forecas ...
* Transport planning and forecasting *
Weather forecasting Weather forecasting is the application of science and technology to predict the conditions of the atmosphere for a given location and time. People have attempted to predict the weather informally for millennia and formally since the 19th cen ...
,
flood forecasting Flood forecasting is the use of forecasted precipitation and streamflow data in rainfall-runoff 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 ...
and
meteorology Meteorology is a branch of the atmospheric sciences (which include atmospheric chemistry and physics) with a major focus on weather forecasting. The study of meteorology dates back millennia, though significant progress in meteorology did no ...


Forecasting as training, betting and futarchy

In several cases, the forecast is either more or less than a prediction of the future. In Philip E. Tetlock's '' Superforecasting: The Art and Science of Prediction'', he discusses forecasting as a method of improving the ability to make decisions. A person can become better calibrated - ie having things they give 10% credence to happening 10% of the time. Or they can forecast things more confidently - coming to the same conclusion but earlier. Some have claimed that that forecasting is a transferrable skill with benefits to other areas of discussion and decision making.
Betting Gambling (also known as betting or gaming) is the wagering of something of value ("the stakes") on a random event with the intent of winning something else of value, where instances of strategy are discounted. Gambling thus requires three elem ...
on sports or politics is another form of forecasting. Rather than being used as advice, bettors are paid based on if they predicted correctly. While decisions might be made based on these bets (forecasts), the main motivation is generally financial. Finally, futarchy is a form of government where forecasts of the impact of government action are used to decide which actions are taken. Rather than advice, in futarchy's strongest form, the action with the best forecasted result is automatically taken.


Forecast improvements

Forecast improvement projects have been operated in a number of sectors: the
National Hurricane Center The National Hurricane Center (NHC) is the division of the United States' NOAA/National Weather Service responsible for tracking and predicting tropical weather systems between the Prime Meridian and the 140th meridian west poleward to the 3 ...
's Hurricane Forecast Improvement Project (HFIP) and the Wind Forecast Improvement Project sponsored by the
US Department of Energy The United States Department of Energy (DOE) is an executive department of the U.S. federal government that oversees U.S. national energy policy and manages the research and development of nuclear power and nuclear weapons in the United States. ...
are examples. In relation to supply chain management, the Du Pont model has been used to show that an increase in forecast accuracy can generate increases in sales anbd reductions in inventory, operating expenses and commitment of working capital.


Categories of forecasting methods


Qualitative vs. quantitative methods

Qualitative forecasting techniques are subjective, based on the opinion and judgment of consumers and experts; they are appropriate when past data are not available. They are usually applied to intermediate- or long-range decisions. Examples of qualitative forecasting methods are informed opinion and judgment, the Delphi method,
market research Market research is an organized effort to gather information about target markets and customers: know about them, starting with who they are. It is an important component of business strategy and a major factor in maintaining competitiveness. Ma ...
, and historical life-cycle analogy. Quantitative forecasting
models A model is an informative representation of an object, person or system. The term originally denoted the plans of a building in late 16th-century English, and derived via French and Italian ultimately from Latin ''modulus'', a measure. Models c ...
are used to forecast future data as a function of past data. They are appropriate to use when past numerical data is available and when it is reasonable to assume that some of the patterns in the data are expected to continue into the future. These methods are usually applied to short- or intermediate-range decisions. Examples of quantitative forecasting methods are last period demand, simple and weighted N-Period moving averages, simple exponential smoothing, poisson process model based forecasting and multiplicative seasonal indexes. Previous research shows that different methods may lead to different level of forecasting accuracy. For example, GMDH neural network was found to have better forecasting performance than the classical forecasting algorithms such as Single Exponential Smooth, Double Exponential Smooth, ARIMA and back-propagation neural network.


Average approach

In this approach, the predictions of all future values are equal to the mean of the past data. This approach can be used with any sort of data where past data is available. In time series notation: :\hat_ = \bar = ( y_1 + ... + y_T ) / T where y_1, ... , y_T is the past data. Although the time series notation has been used here, the average approach can also be used for cross-sectional data (when we are predicting unobserved values; values that are not included in the data set). Then, the prediction for unobserved values is the average of the observed values.


Naïve approach

Naïve forecasts are the most cost-effective forecasting model, and provide a benchmark against which more sophisticated models can be compared. This forecasting method is only suitable for time series
data In the pursuit of knowledge, data (; ) is a collection of discrete values that convey information, describing quantity, quality, fact, statistics, other basic units of meaning, or simply sequences of symbols that may be further interpret ...
. Using the naïve approach, forecasts are produced that are equal to the last observed value. This method works quite well for economic and financial time series, which often have patterns that are difficult to reliably and accurately predict. If the time series is believed to have seasonality, the seasonal naïve approach may be more appropriate where the forecasts are equal to the value from last season. In time series notation: :\hat_ = y_T


Drift method

A variation on the naïve method is to allow the forecasts to increase or decrease over time, where the amount of change over time (called the
drift Drift or Drifts may refer to: Geography * Drift or ford (crossing) of a river * Drift, Kentucky, unincorporated community in the United States * In Cornwall, England: ** Drift, Cornwall, village ** Drift Reservoir, associated with the village ...
) is set to be the average change seen in the historical data. So the forecast for time T+h is given by :\hat_ = y_T + \frac\sum_^T (y_-y_) = y_+h\left(\frac\right). This is equivalent to drawing a line between the first and last observation, and extrapolating it into the future.


Seasonal naïve approach

The seasonal naïve method accounts for seasonality by setting each prediction to be equal to the last observed value of the same season. For example, the prediction value for all subsequent months of April will be equal to the previous value observed for April. The forecast for time T + h is :\hat_ = y_ where m=seasonal period and k is the smallest integer greater than (h-1) / m. The seasonal naïve method is particularly useful for data that has a very high level of seasonality.


Time series methods

Time series In mathematics, a time series is a series of data points indexed (or listed or graphed) in time order. Most commonly, a time series is a sequence taken at successive equally spaced points in time. Thus it is a sequence of discrete-time data. Ex ...
methods use historical data as the basis of estimating future outcomes. They are based on the assumption that past demand history is a good indicator of future demand. * Moving average * Weighted moving average * Exponential smoothing * Autoregressive moving average (ARMA) (forecasts depend on past values of the variable being forecast and on past prediction errors) * Autoregressive integrated moving average (ARIMA) (ARMA on the period-to-period change in the forecast variable) :e.g. Box–Jenkins :Seasonal ARIMA or SARIMA or ARIMARCH, * Extrapolation * Linear prediction * Trend estimation (predicting the variable as a linear or polynomial function of time) * Growth curve (statistics) * Recurrent neural network


Relational methods

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. Several informal methods used in causal forecasting do not rely solely on the output of mathematical
algorithm In mathematics and computer science, an algorithm () is a finite sequence of rigorous instructions, typically used to solve a class of specific problems or to perform a computation. Algorithms are used as specifications for performing ...
s, 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. Causal methods include: *
Regression analysis In statistical modeling, regression analysis is a set of statistical processes for estimating the relationships between a dependent variable (often called the 'outcome' or 'response' variable, or a 'label' in machine learning parlance) and one ...
includes a large group of methods for predicting future values of a variable using information about other variables. These methods include both parametric (linear or non-linear) and non-parametric techniques. * Autoregressive moving average with exogenous inputs (ARMAX) Quantitative forecasting models are often judged against each other by comparing their in-sample or out-of-sample
mean square error In statistics, the mean squared error (MSE) or mean squared deviation (MSD) of an estimator (of a procedure for estimating an unobserved quantity) measures the average of the squares of the errors—that is, the average squared difference between ...
, although some researchers have advised against this. Different forecasting approaches have different levels of accuracy. For example, it was found in one context that GMDH has higher forecasting accuracy than traditional ARIMA.


Judgmental methods

Judgmental forecasting methods incorporate intuitive judgement, opinions and subjective
probability Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, ...
estimates. Judgmental forecasting is used in cases where there is a lack of historical data or during completely new and unique market conditions. Judgmental methods include: *Composite forecasts *Cooke's method * Delphi method *
Forecast by analogy Forecast 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 n ...
* Scenario building *
Statistical survey Survey methodology is "the study of survey methods". As a field of applied statistics concentrating on human-research surveys, survey methodology studies the sampling of individual units from a population and associated techniques of survey da ...
s * Technology forecasting


Artificial intelligence methods

*
Artificial neural networks Artificial neural networks (ANNs), usually simply called neural networks (NNs) or neural nets, are computing systems inspired by the biological neural networks that constitute animal brains. An ANN is based on a collection of connected units ...
* Group method of data handling *
Support vector machine In machine learning, support vector machines (SVMs, also support vector networks) are supervised learning models with associated learning algorithms that analyze data for classification and regression analysis. Developed at AT&T Bell Laborat ...
s Often these are done today by specialized programs loosely labeled * Data mining *
Machine learning Machine learning (ML) is a field of inquiry devoted to understanding and building methods that 'learn', that is, methods that leverage data to improve performance on some set of tasks. It is seen as a part of artificial intelligence. Machine ...
*
Pattern recognition Pattern recognition is the automated recognition of patterns and regularities in data. It has applications in statistical data analysis, signal processing, image analysis, information retrieval, bioinformatics, data compression, computer graphics ...


Geometric extrapolation with error prediction

Can be created with 3 points of a sequence and the "moment" or "index". This type of extrapolation has 100% accuracy in predictions in a big percentage of known series database (OEIS).


Other methods

*
Granger causality The Granger causality test is a statistical hypothesis test for determining whether one time series is useful in forecasting another, first proposed in 1969. Ordinarily, regressions reflect "mere" correlations, but Clive Granger argued that cau ...
*
Simulation A simulation is the imitation of the operation of a real-world process or system over time. Simulations require the use of Conceptual model, models; the model represents the key characteristics or behaviors of the selected system or proc ...
*
Prediction market Prediction markets (also known as betting markets, information markets, decision markets, idea futures or event derivatives) are open markets where specific outcomes can be predicted using financial incentives. Essentially, they are exchange-trad ...
*
Probabilistic forecasting Probabilistic forecasting summarizes what is known about, or opinions about, future events. In contrast to single-valued forecasts (such as forecasting that the maximum temperature at a given site on a given day will be 23 degrees Celsius, or that t ...
and
Ensemble forecasting Ensemble forecasting is a method used in or within numerical weather prediction. Instead of making a single forecast of the most likely weather, a set (or ensemble) of forecasts is produced. This set of forecasts aims to give an indication of the ...


Forecasting accuracy

The forecast error (also known as a residual) is the difference between the actual value and the forecast value for the corresponding period: :\ E_t = Y_t - F_t 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. A good forecasting method will yield residuals that are uncorrelated. If there are
correlation In statistics, correlation or dependence is any statistical relationship, whether causal or not, between two random variables or bivariate data. Although in the broadest sense, "correlation" may indicate any type of association, in statistic ...
s between residual values, then there is information left in the residuals which should be used in computing forecasts. This can be accomplished by computing the expected value of a residual as a function of the known past residuals, and adjusting the forecast by the amount by which this expected value differs from zero. A good forecasting method will also have zero mean. If the residuals have a mean other than zero, then the forecasts are biased and can be improved by adjusting the forecasting technique by an additive constant that equals the mean of the unadjusted residuals. Measures of aggregate error:


Scaled-dependent errors

The forecast error, E, is on the same scale as the data, as such, these accuracy measures are scale-dependent and cannot be used to make comparisons between series on different scales. Mean absolute error (MAE) or mean absolute deviation (MAD): \ MAE = MAD = \frac
Mean squared error In statistics, the mean squared error (MSE) or mean squared deviation (MSD) of an estimator (of a procedure for estimating an unobserved quantity) measures the average of the squares of the errors—that is, the average squared difference between ...
(MSE) or
mean squared prediction error In statistics the mean squared prediction error or mean squared error of the predictions of a smoothing or curve fitting procedure is the expected value of the squared difference between the fitted values implied by the predictive function \wid ...
(MSPE): \ MSE = MSPE = \frac Root mean squared error (RMSE): \ RMSE = \sqrt Average of Errors (E): \ \bar= \frac


Percentage errors

These are more frequently used to compare forecast performance between different data sets because they are scale-independent. However, they have the disadvantage of being extremely large or undefined if Y is close to or equal to zero.
Mean absolute percentage error The mean absolute percentage error (MAPE), also known as mean absolute percentage deviation (MAPD), is a measure of prediction accuracy of a forecasting method in statistics. It usually expresses the accuracy as a ratio defined by the formula: : ...
(MAPE): \ MAPE = 100* \frac Mean absolute percentage deviation (MAPD): \ MAPD = \frac


Scaled errors

Hyndman and Koehler (2006) proposed using scaled errors as an alternative to percentage errors. Mean absolute scaled error (MASE): MASE = \frac where ''m''=seasonal period or 1 if non-seasonal


Other measures

Forecast skill In the fields of forecasting and prediction, forecast skill or prediction skill is any measure of the accuracy and/or degree of association of prediction to an observation or estimate of the actual value of what is being predicted (formally, the pre ...
(SS): \ SS = 1- \frac Business forecasters and practitioners sometimes use different terminology. They refer to the PMAD as the MAPE, although they compute this as a volume weighted MAPE. For more information, see Calculating demand forecast accuracy. When comparing the accuracy of different forecasting methods on a specific data set, the measures of aggregate error are compared with each other and the method that yields the lowest error is preferred.


Training and test sets

When evaluating the quality of forecasts, it is invalid to look at how well a model fits the historical data; the accuracy of forecasts can only be determined by considering how well a model performs on new data that were not used when fitting the model. When choosing models, it is common to use a portion of the available data for fitting, and use the rest of the data for testing the model, as was done in the above examples.


Cross-validation

Cross-validation is a more sophisticated version of training a test set. For
cross-sectional data Cross-sectional data, or a cross section of a study population, in statistics and econometrics, is a type of data collected by observing many subjects (such as individuals, firms, countries, or regions) at the one point or period of time. The anal ...
, one approach to cross-validation works as follows: # Select observation ''i'' for the test set, and use the remaining observations in the training set. Compute the error on the test observation. # Repeat the above step for ''i'' = 1,2,..., ''N'' where ''N'' is the total number of observations. # Compute the forecast accuracy measures based on the errors obtained. This makes efficient use of the available data, as only one observation is omitted at each step For time series data, the training set can only include observations prior to the test set. Therefore, no future observations can be used in constructing the forecast. Suppose ''k'' observations are needed to produce a reliable forecast; then the process works as follows: # Starting with ''i''=1, select the observation ''k + i'' for the test set, and use the observations at times 1, 2, ..., ''k+i''–1 to estimate the forecasting model. Compute the error on the forecast for ''k+i''. # Repeat the above step for ''i'' = 2,...,''T–k'' where ''T'' is the total number of observations. # Compute the forecast accuracy over all errors. This procedure is sometimes known as a "rolling forecasting origin" because the "origin" (''k+i -1)'' at which the forecast is based rolls forward in time. Further, two-step-ahead or in general ''p''-step-ahead forecasts can be computed by first forecasting the value immediately after the training set, then using this value with the training set values to forecast two periods ahead, etc. ''See also'' * Calculating demand forecast accuracy *
Consensus forecasts Used in 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 ...
*
Forecast error In 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. Since the forecast error is derived from the same scale of data, comparisons bet ...
*
Predictability Predictability 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 Causal determinism has a strong relationship with predictability. Per ...
*
Prediction interval In statistical inference, specifically predictive inference, a prediction interval is an estimate of an interval in which a future observation will fall, with a certain probability, given what has already been observed. Prediction intervals are ...
s, similar to
confidence interval In frequentist statistics, a confidence interval (CI) is a range of estimates for an unknown parameter. A confidence interval is computed at a designated ''confidence level''; the 95% confidence level is most common, but other levels, such as 9 ...
s *
Reference class forecasting Reference class forecasting or comparison class forecasting is a method of predicting the future by looking at similar past situations and their outcomes. The theories behind reference class forecasting were developed by Daniel Kahneman and Amos T ...


Seasonality and cyclic behaviour


Seasonality

Seasonality is a characteristic of a time series in which the data experiences regular and predictable changes which recur every calendar year. Any predictable change or pattern in a time series that recurs or repeats over a one-year period can be said to be seasonal. It is common in many situations – such as grocery store or even in a Medical Examiner's office—that the demand depends on the day of the week. In such situations, the forecasting procedure calculates the seasonal index of the “season” – seven seasons, one for each day – which is the ratio of the average demand of that season (which is calculated by Moving Average or Exponential Smoothing using historical data corresponding only to that season) to the average demand across all seasons. An index higher than 1 indicates that demand is higher than average; an index less than 1 indicates that the demand is less than the average.


Cyclic behaviour

The cyclic behaviour of data takes place when there are regular fluctuations in the data which usually last for an interval of at least two years, and when the length of the current cycle cannot be predetermined. Cyclic behavior is not to be confused with seasonal behavior. Seasonal fluctuations follow a consistent pattern each year so the period is always known. As an example, during the Christmas period, inventories of stores tend to increase in order to prepare for Christmas shoppers. As an example of cyclic behaviour, the population of a particular natural ecosystem will exhibit cyclic behaviour when the population decreases as its natural food source decreases, and once the population is low, the food source will recover and the population will start to increase again. Cyclic data cannot be accounted for using ordinary seasonal adjustment since it is not of fixed period.


Limitations

Limitations pose barriers beyond which forecasting methods cannot reliably predict. There are many events and values that cannot be forecast reliably. Events such as the roll of a die or the results of the lottery cannot be forecast because they are random events and there is no significant relationship in the data. When the factors that lead to what is being forecast are not known or well understood such as in
stock In finance, stock (also capital stock) consists of all the shares by which ownership of a corporation or company is divided.Longman Business English Dictionary: "stock - ''especially AmE'' one of the shares into which ownership of a compan ...
and
foreign exchange market The foreign exchange market (Forex, FX, or currency market) is a global decentralized or over-the-counter (OTC) market for the trading of currencies. This market determines foreign exchange rates for every currency. It includes all as ...
s forecasts are often inaccurate or wrong as there is not enough data about everything that affects these markets for the forecasts to be reliable, in addition the outcomes of the forecasts of these markets change the behavior of those involved in the market further reducing forecast accuracy. The concept of "self-destructing predictions" concerns the way in which some predictions can undermine themselves by influencing social behavior. This is because "predictors are part of the social context about which they are trying to make a prediction and may influence that context in the process". For example, a forecast that a large percentage of a population will become HIV infected based on existing trends may cause more people to avoid risky behavior and thus reduce the HIV infection rate, invalidating the forecast (which might have remained correct if it had not been publicly known). Or, a prediction that cybersecurity will become a major issue may cause organizations to implement more security cybersecurity measures, thus limiting the issue.


Performance limits of fluid dynamics equations

As proposed by
Edward Lorenz Edward Norton Lorenz (May 23, 1917 – April 16, 2008) was an American mathematician and meteorologist who established the theoretical basis of weather and climate predictability, as well as the basis for computer-aided atmospheric physics and ...
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 chaotic nature of the
fluid dynamics In physics and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids— liquids and gases. It has several subdisciplines, including ''aerodynamics'' (the study of air and other gases in motion) a ...
equations involved. Extremely small errors in the initial input, such as temperatures and winds, within numerical models double every five days.


See also

*
Accelerating change In futures studies and the history of technology, accelerating change is the observed exponential nature of the rate of technological change in recent history, which may suggest faster and more profound change in the future and may or may not be ...
*
Cash flow forecasting Cash flow forecasting is the process of obtaining an estimate or forecast of a company's future financial position; the cash flow forecast is typically based on anticipated payments and receivables. See Financial forecast for general discussion ...
*
Cliodynamics Cliodynamics () is a transdisciplinary area of research that integrates cultural evolution, economic history/cliometrics, macrosociology, the mathematical modeling of historical processes during the '' longue durée'', and the construction and anal ...
* Collaborative planning, forecasting, and replenishment *
Earthquake prediction Earthquake prediction is a branch of the science of seismology concerned with the specification of the time, location, and magnitude of future earthquakes within stated limits, and particularly "the determination of parameters for the ''next'' ...
* Energy forecasting * Financial forecast * Forecasting bias * Foresight (future studies) *
Frequency spectrum The power spectrum S_(f) of a time series x(t) describes the distribution of power into frequency components composing that signal. According to Fourier analysis, any physical signal can be decomposed into a number of discrete frequencies, ...
*
Futures studies Futures studies, futures research, futurism or futurology is the systematic, interdisciplinary and holistic study of social and technological advancement, and other environmental trends, often for the purpose of exploring how people will l ...
*
Futurology Futures studies, futures research, futurism or futurology is the systematic, interdisciplinary and holistic study of social and technological advancement, and other environmental trends, often for the purpose of exploring how people will li ...
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Kondratiev wave In economics, Kondratiev waves (also called supercycles, great surges, long waves, K-waves or the long economic cycle) are hypothesized cycle-like phenomena in the modern world economy. The phenomenon is closely connected with the technology li ...
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Least squares The method of least squares is a standard approach in regression analysis to approximate the solution of overdetermined systems (sets of equations in which there are more equations than unknowns) by minimizing the sum of the squares of the re ...
* Least-squares spectral analysis *
Optimism bias Optimism bias (or the optimistic bias) is a cognitive bias that causes someone to believe that they themselves are less likely to experience a negative event. It is also known as unrealistic optimism or comparative optimism. Optimism bias is commo ...
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Planning Planning is the process of thinking regarding the activities required to achieve a desired goal. Planning is based on foresight, the fundamental capacity for mental time travel. The evolution of forethought, the capacity to think ahead, is c ...
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Prediction A prediction (Latin ''præ-'', "before," and ''dicere'', "to say"), or forecast, is a statement about a future event or data. They are often, but not always, based upon experience or knowledge. There is no universal agreement about the exact ...
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Predictive analytics Predictive analytics encompasses a variety of statistical techniques from data mining, predictive modeling, and machine learning that analyze current and historical facts to make predictions about future or otherwise unknown events. In busine ...
* Risk management *
Scenario planning Scenario planning, scenario thinking, scenario analysis, scenario prediction and the scenario method all describe a strategic planning method that some organizations use to make flexible long-term plans. It is in large part an adaptation and gener ...
* Spending wave *
Strategic foresight Strategic foresight is a planning-oriented discipline related to futures studies. In a business context, a more action-oriented approach has become well known as corporate foresight.Rohrbeck, Rene (2010) ''Corporate Foresight: Towards a Maturity Mo ...
* Technology forecasting * Thucydides Trap *
Time series In mathematics, a time series is a series of data points indexed (or listed or graphed) in time order. Most commonly, a time series is a sequence taken at successive equally spaced points in time. Thus it is a sequence of discrete-time data. Ex ...
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Weather forecasting Weather forecasting is the application of science and technology to predict the conditions of the atmosphere for a given location and time. People have attempted to predict the weather informally for millennia and formally since the 19th cen ...
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Wind power forecasting A wind power forecast corresponds to an estimate of the expected production of one or more wind turbines (referred to as a wind farm) in the near future, up to a year. Forecast are usually expressed in terms of the available power of the wind far ...


References


Sources

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External links

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Forecasting Principles: ''"Evidence-based forecasting"''International Institute of Forecasters
- A practical guide to Time series analysis and forecasting
Global Forecasting with IFsEarthquake Electromagnetic Precursor Research
{{Authority control Statistical forecasting Supply chain analytics Supply chain management Time series