2988:– 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.
2997:
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.
3019:
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.
555:. 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:
68:
interest is itself forecast. A forecast is not to be confused with a Budget; budgets are more specific, fixed-term financial plans used for resource allocation and control, while forecasts provide estimates of future financial performance, allowing for flexibility and adaptability to changing circumstances. Both tools are valuable in financial planning and decision-making, but they serve different functions.
5340:
118:. 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.
4451:
1610:, 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.
4468:
156:. 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.
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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".
1859:
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
1602:
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
76:
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,
2987:
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
1514:
This approach has been proposed to simulate bursts of seemingly stochastic activity, interrupted by quieter periods. The assumption is that the presence of a strong deterministic ingredient is hidden by noise. The deterministic approach is noteworthy as it can reveal the underlying dynamical systems
67:
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
2821:
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
326:
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
2996:
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
121:
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
3014:
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.
3005:
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
342:
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
542:
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.
883:
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
277:
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 forecasting is a transferable skill with benefits to other areas of discussion and decision making.
1228:
870:
122:
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.
137:
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.
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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.
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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.
292:
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.
1603:
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.
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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.
1867:. 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.
152:— 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
2083:
1103:
482:
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665:
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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.
1980:
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551:
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
77:
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.
5185:
364:
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:
4449:, Berglund, Ulf Stefan & Lundberg, Bjorn Henry, "Comfort control system incorporating weather forecast data and a method for operating such a system", issued August 8, 2000
1299:
1108:
2927:-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.
2805:
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
1509:
1001:
351:, 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,
5446:
5376:
2515:
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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.
1743:
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).
1457:{\displaystyle {\begin{aligned}{\left\{{\begin{array}{ll}x_{t+1}=\alpha f_{n}(x_{t})+\gamma \,y_{t}+\delta \\y_{t+1}=\beta \,y_{t}-\mu \,x_{t}+\eta \end{array}}\right.}\end{aligned}}}
619:
3064:
1843:
4335:
Kaligasidis, Angela Sasic; Taesler, Roger; Andersson, Cari; Nord, Margitta (August 2006). "Upgraded weather forecast control of building heating systems". In Fazio, Paul (ed.).
1097:
A deterministic approach is when there is no stochastic variable involved and the forecasts depend on the selected functions and parameters. For example, given the function
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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
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has been used to show that an increase in forecast accuracy can generate increases in sales and reductions in inventory, operating expenses and commitment of working capital.
537:
269:
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49:
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
1641:, although some researchers have advised against this. Different forecasting approaches have different levels of accuracy. For example, it was found in one context that
1526:
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.
1084:
3423:
3031:
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
1286:
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908:
657:
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29:
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
3556:
Li, Rita Yi Man; Fong, Simon; Chong, Kyle Weng Sang (2017). "Forecasting the REITs and stock indices: Group Method of Data
Handling Neural Network approach".
3357:
5432:
2377:
2270:
5362:
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estimates. Judgmental forecasting is used in cases where there is a lack of historical data or during completely new and unique market conditions.
1545:
4044:
Omalu, B. I.; Shakir, A. M.; Lindner, J. L.; Tayur, S. R. (2007). "Forecasting as an
Operations Management Tool in a Medical Examiner's Office".
3039:
equations involved. Extremely small errors in the initial input, such as temperatures and winds, within numerical models double every five days.
1620:
includes a large group of methods for predicting future values of a variable using information about other variables. These methods include both
629:
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
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1223:{\displaystyle {\begin{aligned}f_{n}(x_{t})={\dfrac {1}{(1+x_{t}^{n})}}\,,\qquad n\in {\mathbb {N} },\;x\in {\mathbb {R} }.\end{aligned}}}
57:
times, while the term "prediction" is used for more general estimates, such as the number of times floods will occur over a long period.
5221:
1994:
865:{\displaystyle {\hat {y}}_{T+h|T}=y_{T}+{\frac {h}{T-1}}\sum _{t=2}^{T}(y_{t}-y_{t-1})=y_{T}+h\left({\frac {y_{T}-y_{1}}{T-1}}\right).}
370:
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2179:
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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.
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5542:
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4809:
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intermediate-range decisions. Examples of quantitative forecasting methods are last period demand, simple and weighted N-Period
5547:
3124:
5200:
4814:
2264:
227:
3302:, A list of collated exchange rate forecasts encompassing technical and fundamental analysis in the foreign exchange market.
273:, he discusses forecasting as a method of improving the ability to make decisions. A person can become better calibrated —
3006:
relationship in the data. When the factors that lead to what is being forecast are not known or well understood such as in
4619:
2830:
1988:
1707:
352:
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1470:
916:
5205:
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96:
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for the test set, and use the remaining observations in the training set. Compute the error on the test observation.
2677:{\displaystyle MASE={\frac {\sum _{t=1}^{N}|{\frac {E_{t}}{{\frac {1}{N-m}}\sum _{t=m+1}^{N}|Y_{t}-Y_{t-m}|}}|}{N}}}
5195:
4950:
3368:
3094:
2509:
2087:
1885:
1702:
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This is equivalent to drawing a line between the first and last observation, and extrapolating it into the future.
236:
1848:
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.
1637:
Quantitative forecasting models are often judged against each other by comparing their in-sample or out-of-sample
5063:
4955:
4687:
1767:
1586:
302:
17:
3508:
The Wind
Forecast Improvement Project (WFIP): A Public–Private Partnership Addressing Wind Energy Forecast Needs
33:
their revenue in the next year, then compare it against the actual results creating a variance actual analysis.
5507:
5317:
5073:
4537:
1625:
1591:
149:
89:
561:
103:
is common. Such analysis is provided by both non-profit groups as well as by for-profit private institutions.
305:'s Hurricane Forecast Improvement Project (HFIP) and the Wind Forecast Improvement Project sponsored by the
84:
for buildings. This attempts to reduce the energy needed to heat the building, thus reducing the emission of
37:
is a similar but more general term. Forecasting might refer to specific formal statistical methods employing
5252:
5098:
5058:
4896:
4760:
4624:
4597:
4587:
3609:
3264:
Helen Allen; Mark P. Taylor (1990). "Charts, Noise and
Fundamentals in the London Foreign Exchange Market".
3011:
1535:
306:
145:
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3189:
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1712:
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222:
53:
the terms "forecast" and "forecasting" are sometimes reserved for estimates of values at certain specific
4472:
3311:
T. Chadefaux (2014). "Early warning signals for war in the news". Journal of Peace
Research, 51(1), 5-18
1792:
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Several informal methods used in causal forecasting do not rely solely on the output of mathematical
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The seasonal naïve method is particularly useful for data that has a very high level of seasonality.
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197:
159:
115:
100:
42:
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1786:) is the difference between the actual value and the forecast value for the corresponding period:
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1984:
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111:
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While the veracity of predictions for actual stock returns are disputed through reference to the
46:
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This makes efficient use of the available data, as only one observation is omitted at each step
2506:
Hyndman and
Koehler (2006) proposed using scaled errors as an alternative to percentage errors.
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Forecasting the REITs and stock indices: Group Method of Data
Handling Neural Network approach
3896:
3820:
3795:
3770:
3752:
3693:
3675:
3533:
Mahmud, Tahmida; Hasan, Mahmudul; Chakraborty, Anirban; Roy-Chowdhury, Amit (19 August 2016).
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1762:
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1548:(forecasts depend on past values of the variable being forecast and on past prediction errors)
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at which the forecast is based rolls forward in time. Further, two-step-ahead or in general
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630:
125:
An important, albeit often ignored aspect of forecasting, is the relationship it holds with
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observations are needed to produce a reliable forecast; then the process works as follows:
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3467:"Relative Accuracy of Judgmental and Extrapolative Methods in Forecasting Annual Earnings"
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3149:
3114:
3104:
2919:
This procedure is sometimes known as a "rolling forecasting origin" because the "origin" (
332:
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887:
636:
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Judgmental forecasting methods incorporate intuitive judgement, opinions and subjective
633:) is set to be the average change seen in the historical data. So the forecast for time
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In several cases, the forecast is either more or less than a prediction of the future.
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107:
4427:(2007). "Scientific Prediction in Historical Sociology: Ibn Khaldun meets Al Saud".
4065:
3493:
3394:"Role thinking: Standing in other people's shoes to forecast decisions in conflicts"
5424:
4429:
History & Mathematics: Historical
Dynamics and Development of Complex Societies
3634:
Stoop, Ruedi; Orlando, Giuseppe; Bufalo, Michele; Della Rossa, Fabio (2022-11-18).
3059:
3032:
3007:
1515:
structure, which can be exploited for steering the dynamics into a desired regime.
192:
5354:
3845:"Error Measures For Generalizing About Forecasting Methods: Empirical Comparisons"
3569:
3223:
4497:
3299:
4029:
4012:
3713:"Financial markets' deterministic aspects modeled by a low-dimensional equation"
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1856:
1722:
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1523:
249:
64:
38:
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2492:{\displaystyle \ MAPD={\frac {\sum _{t=1}^{N}|E_{t}|}{\sum _{t=1}^{N}|Y_{t}|}}}
2365:{\displaystyle \ MAPE=100*{\frac {\sum _{t=1}^{N}|{\frac {E_{t}}{Y_{t}}}|}{N}}}
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4553:
3937:
3542:
3139:
3109:
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1308:
34:
30:
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3938:"Probnet: Geometric Extrapolation of Integer Sequences with error prediction"
3756:
3679:
301:
Forecast improvement projects have been operated in a number of sectors: the
5043:
4886:
3507:
2893:–1 to estimate the forecasting model. Compute the error on the forecast for
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50:
3774:
3697:
3485:
4467:
3358:"The Ombudsman: Value of Expertise for Forecasting Decisions in Conflicts"
4110:
4013:"Enterprise-Wide Optimization of Total Landed Cost at a Grocery Retailer"
3670:
3134:
289:
126:
4512:
4478:
4175:
Principles of Forecasting: A Handbook for Researchers and Practitioners
3537:. 2016 IEEE International Conference on Image Processing (ICIP). IEEE.
3285:
281:
180:
4492:
Introduction to Time series Analysis (Engineering Statistics Handbook)
2167:{\displaystyle \ RMSE={\sqrt {\frac {\sum _{t=1}^{N}{E_{t}^{2}}}{N}}}}
202:
54:
4084:"The geopolitics of renewable energy: Debunking four emerging myths"
3277:
2866:
Compute the forecast accuracy measures based on the errors obtained.
1583:(predicting the variable as a linear or polynomial function of time)
4378:
Predicting the Future: An Introduction to the Theory of Forecasting
1718:
Often these are done today by specialized programs loosely labeled
92:
in everyday business for manufacturing and distribution companies.
80:
Climate change and increasing energy prices have led to the use of
5408:
2078:{\displaystyle \ MSE=MSPE={\frac {\sum _{t=1}^{N}{E_{t}^{2}}}{N}}}
1631:
4395:
Taesler, Roger (1991). "Climate and Building Energy Management".
3969:
3910:
3636:"Exploiting deterministic features in apparently stochastic data"
3601:
3248:
477:{\displaystyle {\hat {y}}_{T+h|T}={\bar {y}}=(y_{1}+...+y_{T})/T}
4356:
Forecasting and Market Analysis Techniques: A Practical Approach
4297:
Makridakis, Spyros; Wheelwrigt, Steven; Hyndman, Rob J. (1998).
3243:
3241:
2889:
for the test set, and use the observations at times 1, 2, ...,
2246:{\displaystyle \ {\bar {E}}={\frac {\sum _{i=1}^{N}{E_{i}}}{N}}}
1642:
552:
60:
5428:
5358:
4526:
3711:
Orlando, Giuseppe; Bufalo, Michele; Stoop, Ruedi (2022-02-01).
5186:
Association of Technology, Management, and Applied Engineering
1554:(ARMA on the period-to-period change in the forecast variable)
4522:
4507:
4486:
1975:{\displaystyle \ MAE=MAD={\frac {\sum _{t=1}^{N}|E_{t}|}{N}}}
129:. Forecasting can be described as predicting what the future
3324:
J. Scott Armstrong; Kesten C. Green; Andreas Graefe (2010).
4494:- A practical guide to Time series analysis and forecasting
1632:
Autoregressive moving average with exogenous inputs (ARMAX)
1446:
4318:
Operations and Production Systems with Multiple Objectives
2796:{\displaystyle \ SS=1-{\frac {MSE_{forecast}}{MSE_{ref}}}}
309:
are examples. In relation to supply chain management, the
110:
movements is typically achieved through a combination of
4502:
2833:
is a more sophisticated version of training a test set.
1851:
A good forecasting method will yield residuals that are
1645:
has higher forecasting accuracy than traditional ARIMA.
3817:
Production Planning and Inventory Control Virginia Tech
4177:. Norwell, Massachusetts: Kluwer Academic Publishers.
3065:
Collaborative planning, forecasting, and replenishment
4339:. Taylor & Francis, CRC Press. pp. 951–958.
4337:
Research in Building Physics and Building Engineering
3788:
Steven Nahmias; Tava Lennon Olsen (15 January 2015).
3510:, published 30 October 2015, accessed 9 December 2022
2840:, one approach to cross-validation works as follows:
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1012:
919:
890:
668:
639:
564:
493:
373:
133:
look like, whereas planning predicts what the future
3899:, Pacific Rim Property Research Journal, 23(2), 1-38
3210:
French, Jordan (2017). "The time traveller's CAPM".
5245:
5214:
5178:
5150:
5122:
5034:
5008:
4936:
4910:
4867:
4835:
4791:
4780:
4726:
4661:
4654:
4643:
4578:
3791:
Production and Operations Analysis: Seventh Edition
270:
Superforecasting: The Art and Science of Prediction
4234:
4134:
3895:16. Li, Rita Yi Man, Fong, S., Chong, W.S. (2017)
2795:
2676:
2491:
2364:
2245:
2166:
2077:
1974:
1837:
1503:
1456:
1280:
1253:
1222:
1078:
1038:
1018:
995:
902:
864:
651:
613:
531:
476:
1504:{\displaystyle \alpha ,\gamma ,\beta ,\mu ,\eta }
996:{\displaystyle {\hat {y}}_{T+h|T}=y_{T+h-m(k+1)}}
3535:A poisson process model for activity forecasting
1552:Autoregressive integrated moving average (ARIMA)
141:Forecasting has application in many situations:
4261:"Another look at measures of forecast accuracy"
3300:"Euro Forecast from Institutional Researchers"
3023:Performance limits of fluid dynamics equations
2915:Compute the forecast accuracy over all errors.
5440:
5370:
4538:
4513:Forecasting Science and Theory of Forecasting
4508:Earthquake Electromagnetic Precursor Research
3595:
3593:
3591:
3589:
3587:
3356:Kesten C. Greene; J. Scott Armstrong (2007).
1739:Geometric extrapolation with error prediction
256:Forecasting as training, betting and futarchy
8:
4259:; Koehler, Anne B. (October–December 2006).
3392:Kesten C. Green; J. Scott Armstrong (1975).
4354:Kress, George J.; Snyder, John (May 1994).
2374:Mean absolute percentage deviation (MAPD):
5447:
5433:
5425:
5377:
5363:
5355:
4788:
4658:
4651:
4545:
4531:
4523:
1199:
23:Making predictions based on available data
4279:
4194:Production Planning and Inventory Control
4109:
4099:
4028:
3971:2.5 Evaluating forecast accuracy | OTexts
3865:
3764:
3746:
3736:
3687:
3669:
3659:
2778:
2739:
2726:
2706:
2663:
2655:
2643:
2630:
2621:
2615:
2598:
2576:
2569:
2563:
2558:
2552:
2541:
2534:
2517:
2481:
2475:
2466:
2460:
2449:
2438:
2432:
2423:
2417:
2406:
2399:
2379:
2351:
2343:
2333:
2327:
2322:
2316:
2305:
2298:
2272:
2230:
2225:
2219:
2208:
2201:
2187:
2186:
2181:
2150:
2145:
2140:
2134:
2123:
2115:
2095:
2062:
2057:
2052:
2046:
2035:
2028:
1996:
1961:
1955:
1946:
1940:
1929:
1922:
1893:
1863:A good forecasting method will also have
1829:
1816:
1803:
1794:
1472:
1430:
1425:
1413:
1408:
1390:
1370:
1365:
1350:
1337:
1315:
1307:
1302:
1298:
1296:
1272:
1266:
1245:
1239:
1208:
1207:
1206:
1191:
1190:
1189:
1178:
1165:
1160:
1140:
1128:
1115:
1107:
1105:
1068:
1051:
1031:
1011:
960:
943:
933:
922:
921:
918:
889:
835:
822:
815:
799:
777:
764:
751:
740:
718:
709:
692:
682:
671:
670:
667:
638:
605:
588:
578:
567:
566:
563:
523:
498:
492:
466:
457:
432:
411:
410:
397:
387:
376:
375:
372:
5489:
3909:Hyndman, Rob J; Athanasopoulos, George.
3600:Hyndman, Rob J; Athanasopoulos, George.
614:{\displaystyle {\hat {y}}_{T+h|T}=y_{T}}
4141:. John Wiley & Sons, Inc. pp.
3964:
3962:
3447:. Forecastingprinciples.com. 1998-02-14
3426:. Forecastingprinciples.com. 1998-02-14
3326:"Answers to Frequently Asked Questions"
3202:
4487:International Institute of Forecasters
4380:. State University of New York Press.
3993:
3983:
2690:=seasonal period or 1 if non-seasonal
1261:and the is the medium-long term trend
4299:Forecasting: Methods and Applications
4216:Predictive Inference: An Introduction
4077:
4075:
3629:
3627:
3602:"2.3 Some simple forecasting methods"
3558:Pacific Rim Property Research Journal
3319:
3317:
1565:Seasonal ARIMA or SARIMA or ARIMARCH,
1046:is the smallest integer greater than
335:, and historical life-cycle analogy.
203:Player and team performance in sports
7:
4268:International Journal of Forecasting
4088:Energy Research & Social Science
3915:Forecasting: Principles and Practice
3853:International Journal of Forecasting
3606:Forecasting: Principles and Practice
3398:International Journal of Forecasting
3250:Forecasting: Principles and Practice
2937:Calculating demand forecast accuracy
2912:is the total number of observations.
2863:is the total number of observations.
2807:Calculating demand forecast accuracy
1782:The forecast error (also known as a
1546:Autoregressive moving average (ARMA)
322:Qualitative vs. quantitative methods
101:forecasting of broad economic trends
5222:Bachelor of Business Administration
4431:. Moscow: KomKniga. pp. 9–38.
4316:Malakooti, Behnam (February 2014).
1838:{\displaystyle \ E_{t}=Y_{t}-F_{t}}
5323:Organizational behavior management
14:
5237:Doctor of Business Administration
5227:Master of Business Administration
4241:. London: John Wiley & Sons.
4218:. Chapman & Hall, CRC Press.
3612:from the original on Aug 13, 2017
317:Categories of forecasting methods
5338:
4466:
4290:10.1016/j.ijforecast.2006.03.001
3070:Computer supported brainstorming
2972:Seasonality and cyclic behaviour
5500:Associative (causal) forecasts
3948:from the original on 2022-08-14
3125:Least-squares spectral analysis
1697:Artificial intelligence methods
1182:
532:{\displaystyle y_{1},...,y_{T}}
177:for renewable power integration
5201:Chartered Management Institute
4082:Overland, Indra (2019-03-01).
2664:
2656:
2622:
2559:
2482:
2467:
2439:
2424:
2352:
2323:
2265:Mean absolute percentage error
2192:
1962:
1947:
1356:
1343:
1171:
1147:
1134:
1121:
1065:
1053:
988:
976:
944:
927:
789:
757:
693:
676:
589:
572:
463:
425:
416:
398:
381:
228:Telecommunications forecasting
1:
4011:Erhun, F.; Tayur, S. (2003).
3570:10.1080/14445921.2016.1225149
3224:10.1080/10293523.2016.1255469
1989:mean squared prediction error
1870:Measures of aggregate error:
1708:Group method of data handling
5485:Decomposition of time series
4570:Index of management articles
4481:"Evidence-based forecasting"
4417:10.1016/0378-7788(91)90028-2
4046:Journal of Health Management
3876:10.1016/0169-2070(92)90008-w
1660:Judgmental methods include:
5206:Critical management studies
5069:Full range leadership model
4518:Measuring Forecast Accuracy
4503:Global Forecasting with IFs
4030:10.1287/opre.51.3.343.14953
3465:J. Scott Armstrong (1983).
3212:Investment Analysts Journal
2966:Reference class forecasting
2885:=1, select the observation
2851:Repeat the above step for
1624:(linear or non-linear) and
97:efficient-market hypothesis
5576:
5466:Historical data forecasts
5196:Certified Business Manager
4233:Gilchrist, Warren (1976).
4101:10.1016/j.erss.2018.10.018
4058:10.1177/097206340700900105
3738:10.1038/s41598-022-05765-z
3661:10.1038/s41598-022-23212-x
3523:, accessed 9 December 2022
3095:Foresight (future studies)
2980:
2900:Repeat the above step for
2510:Mean absolute scaled error
1703:Artificial neural networks
1234:The short term behaviour
15:
5498:
5464:
5394:
5336:
5064:Evidence-based management
4560:
4320:. John Wiley & Sons.
4301:. John Wiley & Sons.
3843:and Fred Collopy (1992).
3543:10.1109/ICIP.2016.7532978
1768:Probabilistic forecasting
1587:Growth curve (statistics)
338:Quantitative forecasting
303:National Hurricane Center
88:. Forecasting is used in
5508:Simple linear regression
5318:Organization development
5074:Management by objectives
4479:Forecasting Principles:
4192:Ellis, Kimberly (2010).
3815:Ellis, Kimberly (2008).
3521:Beyond Basic Forecasting
3012:foreign exchange markets
1613:Causal methods include:
1592:Recurrent neural network
150:customer demand planning
90:customer demand planning
5553:Supply chain management
5543:Statistical forecasting
5099:Social entrepreneurship
5059:Earned value management
4237:Statistical Forecasting
3519:Logility, Inc. (2016),
2176:Average of Errors (E):
2088:Root mean squared error
1886:mean absolute deviation
1874:Scaled-dependent errors
1713:Support vector machines
1536:Weighted moving average
1079:{\displaystyle (h-1)/m}
879:Seasonal naïve approach
307:US Department of Energy
146:Supply chain management
5548:Supply chain analytics
5345:Systems science portal
5288:Management development
5283:Management cybernetics
5268:Executive compensation
5104:Sustainable management
4966:Information technology
4946:Environmental resource
3506:Department of Energy,
3486:10.1002/for.3980020411
3474:Journal of Forecasting
3367:: 1–12. Archived from
3190:Wind power forecasting
3170:Technology forecasting
2817:Training and test sets
2797:
2678:
2620:
2557:
2493:
2465:
2422:
2366:
2321:
2247:
2224:
2168:
2139:
2079:
2051:
1976:
1945:
1839:
1691:Technology forecasting
1505:
1458:
1282:
1255:
1224:
1093:Deterministic approach
1080:
1040:
1020:
997:
904:
866:
756:
653:
615:
533:
478:
223:Technology forecasting
5475:Exponential smoothing
5308:Managerial psychology
5273:Management consulting
5094:Scientific management
4877:Customer relationship
4565:Outline of management
4447:US patent 6098893
4133:Cox, John D. (2002).
3936:V. Nos (2021-06-02).
3298:Pound Sterling Live.
3075:Earthquake prediction
3055:Cash flow forecasting
2798:
2679:
2594:
2537:
2494:
2445:
2402:
2367:
2301:
2248:
2204:
2169:
2119:
2080:
2031:
1977:
1925:
1840:
1541:Exponential smoothing
1511:are some parameters.
1506:
1459:
1283:
1281:{\displaystyle y_{t}}
1256:
1254:{\displaystyle x_{t}}
1225:
1081:
1041:
1026:=seasonal period and
1021:
998:
905:
867:
736:
654:
616:
534:
479:
349:exponential smoothing
297:Forecast improvements
208:Political forecasting
165:Earthquake prediction
5303:Managerial economics
5263:Corporate governance
5170:Oliver E. Williamson
5049:Collaborative method
4498:Time Series Analysis
4475:at Wikimedia Commons
4397:Energy and Buildings
3266:The Economic Journal
3145:Predictive analytics
3080:Economic forecasting
2961:confidence intervals
2957:Prediction intervals
2838:cross-sectional data
2705:
2516:
2378:
2271:
2180:
2094:
1995:
1892:
1793:
1778:Forecasting accuracy
1772:Ensemble forecasting
1471:
1295:
1265:
1238:
1104:
1050:
1030:
1010:
917:
888:
666:
637:
562:
491:
371:
198:Land use forecasting
160:Economic forecasting
116:fundamental analysis
16:For other uses, see
5513:Regression analysis
5409:Sales force polling
5165:Eliyahu M. Goldratt
4409:1991EneBu..16..599T
4171:Armstrong, J. Scott
4017:Operations Research
3748:20.500.11850/531723
3729:2022NatSR..12.1693O
3652:2022NatSR..1219843S
3185:Weather forecasting
3165:Strategic foresight
3050:Accelerating change
2942:Consensus forecasts
2844:Select observation
2155:
2067:
1882:Mean absolute error
1860:differs from zero.
1733:Pattern recognition
1686:Statistical surveys
1676:Forecast by analogy
1664:Composite forecasts
1618:Regression analysis
1519:Time series methods
1170:
903:{\displaystyle T+h}
652:{\displaystyle T+h}
242:Weather forecasting
213:Product forecasting
5399:Executive opinions
5328:Pointy-haired Boss
5278:Management control
5114:Virtual management
3911:"3.1 Introduction"
3841:J. Scott Armstrong
3794:. Waveland Press.
3717:Scientific Reports
3640:Scientific Reports
3100:Frequency spectrum
3085:Energy forecasting
2793:
2674:
2489:
2362:
2243:
2164:
2141:
2075:
2053:
1985:Mean squared error
1972:
1835:
1649:Judgmental methods
1598:Relational methods
1501:
1454:
1452:
1444:
1278:
1251:
1220:
1218:
1176:
1156:
1076:
1036:
1016:
993:
900:
862:
649:
611:
539:is the past data.
529:
474:
327:and judgment, the
233:Transport planning
175:Energy forecasting
5525:
5524:
5518:Econometric model
5422:
5421:
5352:
5351:
5298:Management system
5232:PhD in management
5004:
5003:
4863:
4862:
4776:
4775:
4744:Product lifecycle
4471:Media related to
4438:978-5-484-01002-8
4387:978-0-7914-3553-3
4374:Rescher, Nicholas
4365:978-0-89930-835-7
4346:978-0-415-41675-7
4327:978-0-470-03732-4
4308:978-0-471-53233-0
4248:978-0-471-99403-9
4225:978-0-390-87106-0
4203:978-0-412-03471-8
4184:978-0-7923-7930-0
4152:978-0-471-38108-2
3826:978-0-390-87106-0
3801:978-1-4786-2824-8
3155:Scenario planning
2791:
2710:
2672:
2661:
2592:
2487:
2383:
2360:
2349:
2276:
2256:Percentage errors
2241:
2195:
2185:
2162:
2161:
2099:
2073:
2000:
1970:
1897:
1798:
1763:Prediction market
1753:Granger causality
1681:Scenario building
1639:mean square error
1576:Linear prediction
1175:
1039:{\displaystyle k}
1019:{\displaystyle m}
930:
853:
734:
679:
575:
419:
384:
265:Philip E. Tetlock
246:flood forecasting
218:Sales forecasting
170:Egain forecasting
82:Egain Forecasting
5565:
5449:
5442:
5435:
5426:
5414:Consumer surveys
5379:
5372:
5365:
5356:
5342:
5079:Management style
4789:
4659:
4652:
4547:
4540:
4533:
4524:
4470:
4455:
4454:
4450:
4442:
4420:
4403:(1–2): 599–608.
4391:
4369:
4358:. Quorum Books.
4350:
4331:
4312:
4293:
4283:
4265:
4252:
4240:
4229:
4212:Geisser, Seymour
4207:
4188:
4157:
4156:
4140:
4130:
4124:
4123:
4113:
4103:
4079:
4070:
4069:
4041:
4035:
4034:
4032:
4008:
4002:
4001:
3995:
3991:
3989:
3981:
3979:
3978:
3966:
3957:
3956:
3954:
3953:
3933:
3927:
3926:
3924:
3922:
3906:
3900:
3893:
3887:
3886:
3884:
3878:. Archived from
3869:
3849:
3837:
3831:
3830:
3812:
3806:
3805:
3785:
3779:
3778:
3768:
3750:
3740:
3708:
3702:
3701:
3691:
3673:
3663:
3631:
3622:
3621:
3619:
3617:
3597:
3582:
3581:
3553:
3547:
3546:
3530:
3524:
3517:
3511:
3504:
3498:
3497:
3471:
3462:
3456:
3455:
3453:
3452:
3445:"Selection Tree"
3441:
3435:
3434:
3432:
3431:
3420:
3414:
3413:
3389:
3383:
3382:
3380:
3379:
3373:
3362:
3353:
3347:
3346:
3344:
3343:
3337:
3331:. Archived from
3330:
3321:
3312:
3309:
3303:
3296:
3290:
3289:
3261:
3255:
3254:
3245:
3236:
3235:
3207:
3090:Forecasting bias
2992:Cyclic behaviour
2831:Cross-validation
2826:Cross-validation
2802:
2800:
2799:
2794:
2792:
2790:
2789:
2788:
2766:
2765:
2764:
2727:
2708:
2683:
2681:
2680:
2675:
2673:
2668:
2667:
2662:
2660:
2659:
2654:
2653:
2635:
2634:
2625:
2619:
2614:
2593:
2591:
2577:
2574:
2573:
2564:
2562:
2556:
2551:
2535:
2498:
2496:
2495:
2490:
2488:
2486:
2485:
2480:
2479:
2470:
2464:
2459:
2443:
2442:
2437:
2436:
2427:
2421:
2416:
2400:
2381:
2371:
2369:
2368:
2363:
2361:
2356:
2355:
2350:
2348:
2347:
2338:
2337:
2328:
2326:
2320:
2315:
2299:
2274:
2252:
2250:
2249:
2244:
2242:
2237:
2236:
2235:
2234:
2223:
2218:
2202:
2197:
2196:
2188:
2183:
2173:
2171:
2170:
2165:
2163:
2157:
2156:
2154:
2149:
2138:
2133:
2117:
2116:
2097:
2084:
2082:
2081:
2076:
2074:
2069:
2068:
2066:
2061:
2050:
2045:
2029:
1998:
1981:
1979:
1978:
1973:
1971:
1966:
1965:
1960:
1959:
1950:
1944:
1939:
1923:
1895:
1844:
1842:
1841:
1836:
1834:
1833:
1821:
1820:
1808:
1807:
1796:
1728:Machine learning
1581:Trend estimation
1510:
1508:
1507:
1502:
1463:
1461:
1460:
1455:
1453:
1449:
1448:
1445:
1435:
1434:
1418:
1417:
1401:
1400:
1375:
1374:
1355:
1354:
1342:
1341:
1326:
1325:
1287:
1285:
1284:
1279:
1277:
1276:
1260:
1258:
1257:
1252:
1250:
1249:
1229:
1227:
1226:
1221:
1219:
1212:
1211:
1195:
1194:
1177:
1174:
1169:
1164:
1142:
1133:
1132:
1120:
1119:
1085:
1083:
1082:
1077:
1072:
1045:
1043:
1042:
1037:
1025:
1023:
1022:
1017:
1002:
1000:
999:
994:
992:
991:
952:
951:
947:
932:
931:
923:
909:
907:
906:
901:
871:
869:
868:
863:
858:
854:
852:
841:
840:
839:
827:
826:
816:
804:
803:
788:
787:
769:
768:
755:
750:
735:
733:
719:
714:
713:
701:
700:
696:
681:
680:
672:
658:
656:
655:
650:
620:
618:
617:
612:
610:
609:
597:
596:
592:
577:
576:
568:
538:
536:
535:
530:
528:
527:
503:
502:
483:
481:
480:
475:
470:
462:
461:
437:
436:
421:
420:
412:
406:
405:
401:
386:
385:
377:
360:Average approach
183:against risk of
108:foreign exchange
86:greenhouse gases
5575:
5574:
5568:
5567:
5566:
5564:
5563:
5562:
5528:
5527:
5526:
5521:
5494:
5460:
5453:
5423:
5418:
5390:
5383:
5353:
5348:
5332:
5241:
5210:
5191:Business school
5174:
5152:
5146:
5132:Decision-making
5124:
5118:
5089:Micromanagement
5084:Macromanagement
5036:
5030:
5000:
4956:Human resources
4951:Field inventory
4932:
4906:
4869:
4859:
4831:
4784:
4782:
4772:
4722:
4665:
4647:
4645:
4639:
4581:of organization
4580:
4574:
4556:
4551:
4463:
4452:
4445:
4439:
4423:
4394:
4388:
4372:
4366:
4353:
4347:
4334:
4328:
4315:
4309:
4296:
4281:10.1.1.154.9771
4263:
4257:Hyndman, Rob J.
4255:
4249:
4232:
4226:
4210:
4204:
4196:. McGraw-Hill.
4191:
4185:
4169:
4166:
4161:
4160:
4153:
4132:
4131:
4127:
4081:
4080:
4073:
4043:
4042:
4038:
4010:
4009:
4005:
3992:
3982:
3976:
3974:
3968:
3967:
3960:
3951:
3949:
3944:. Haskell.org.
3935:
3934:
3930:
3920:
3918:
3908:
3907:
3903:
3894:
3890:
3882:
3847:
3839:
3838:
3834:
3827:
3819:. McGraw Hill.
3814:
3813:
3809:
3802:
3787:
3786:
3782:
3710:
3709:
3705:
3633:
3632:
3625:
3615:
3613:
3599:
3598:
3585:
3555:
3554:
3550:
3532:
3531:
3527:
3518:
3514:
3505:
3501:
3469:
3464:
3463:
3459:
3450:
3448:
3443:
3442:
3438:
3429:
3427:
3422:
3421:
3417:
3391:
3390:
3386:
3377:
3375:
3371:
3360:
3355:
3354:
3350:
3341:
3339:
3335:
3328:
3323:
3322:
3315:
3310:
3306:
3297:
3293:
3278:10.2307/2234183
3263:
3262:
3258:
3247:
3246:
3239:
3209:
3208:
3204:
3199:
3194:
3175:Thucydides Trap
3150:Risk management
3115:Kondratiev wave
3105:Futures studies
3045:
3027:As proposed by
3025:
3003:
2994:
2985:
2979:
2974:
2828:
2819:
2774:
2767:
2735:
2728:
2703:
2702:
2696:
2639:
2626:
2581:
2575:
2565:
2536:
2514:
2513:
2504:
2471:
2444:
2428:
2401:
2376:
2375:
2339:
2329:
2300:
2269:
2268:
2258:
2226:
2203:
2178:
2177:
2118:
2092:
2091:
2030:
1993:
1992:
1951:
1924:
1890:
1889:
1876:
1855:. If there are
1825:
1812:
1799:
1791:
1790:
1780:
1749:
1741:
1699:
1651:
1600:
1521:
1469:
1468:
1451:
1450:
1443:
1442:
1426:
1409:
1386:
1383:
1382:
1366:
1346:
1333:
1311:
1303:
1293:
1292:
1268:
1263:
1262:
1241:
1236:
1235:
1233:
1217:
1216:
1146:
1124:
1111:
1102:
1101:
1095:
1048:
1047:
1028:
1027:
1008:
1007:
956:
920:
915:
914:
886:
885:
881:
842:
831:
818:
817:
811:
795:
773:
760:
723:
705:
669:
664:
663:
635:
634:
627:
601:
565:
560:
559:
549:
519:
494:
489:
488:
453:
428:
374:
369:
368:
362:
345:moving averages
333:market research
324:
319:
299:
258:
74:
43:cross-sectional
24:
21:
12:
11:
5:
5573:
5572:
5569:
5561:
5560:
5555:
5550:
5545:
5540:
5530:
5529:
5523:
5522:
5520:
5515:
5510:
5505:
5503:Moving average
5499:
5496:
5495:
5493:
5492:
5490:Naïve approach
5487:
5482:
5480:Trend analysis
5477:
5472:
5470:Moving average
5465:
5462:
5461:
5454:
5452:
5451:
5444:
5437:
5429:
5420:
5419:
5417:
5416:
5411:
5406:
5401:
5395:
5392:
5391:
5384:
5382:
5381:
5374:
5367:
5359:
5350:
5349:
5337:
5334:
5333:
5331:
5330:
5325:
5320:
5315:
5310:
5305:
5300:
5295:
5293:Management fad
5290:
5285:
5280:
5275:
5270:
5265:
5260:
5255:
5253:Administration
5249:
5247:
5243:
5242:
5240:
5239:
5234:
5229:
5224:
5218:
5216:
5212:
5211:
5209:
5208:
5203:
5198:
5193:
5188:
5182:
5180:
5176:
5175:
5173:
5172:
5167:
5162:
5156:
5154:
5148:
5147:
5145:
5144:
5139:
5134:
5128:
5126:
5120:
5119:
5117:
5116:
5111:
5106:
5101:
5096:
5091:
5086:
5081:
5076:
5071:
5066:
5061:
5056:
5051:
5046:
5040:
5038:
5032:
5031:
5029:
5028:
5023:
5018:
5012:
5010:
5006:
5005:
5002:
5001:
4999:
4998:
4993:
4988:
4983:
4978:
4973:
4968:
4963:
4958:
4953:
4948:
4942:
4940:
4934:
4933:
4931:
4930:
4925:
4920:
4914:
4912:
4908:
4907:
4905:
4904:
4899:
4894:
4889:
4884:
4879:
4873:
4871:
4865:
4864:
4861:
4860:
4858:
4857:
4852:
4847:
4841:
4839:
4833:
4832:
4830:
4829:
4824:
4823:
4822:
4817:
4803:
4797:
4795:
4786:
4781:On activity or
4778:
4777:
4774:
4773:
4771:
4770:
4765:
4764:
4763:
4753:
4752:
4751:
4746:
4736:
4730:
4728:
4724:
4723:
4721:
4720:
4715:
4710:
4705:
4700:
4695:
4690:
4685:
4680:
4675:
4669:
4667:
4656:
4649:
4641:
4640:
4638:
4637:
4632:
4627:
4622:
4617:
4612:
4607:
4606:
4605:
4595:
4590:
4584:
4582:
4576:
4575:
4573:
4572:
4567:
4561:
4558:
4557:
4552:
4550:
4549:
4542:
4535:
4527:
4521:
4520:
4515:
4510:
4505:
4500:
4495:
4489:
4484:
4476:
4462:
4461:External links
4459:
4458:
4457:
4443:
4437:
4425:Turchin, Peter
4421:
4392:
4386:
4370:
4364:
4351:
4345:
4332:
4326:
4313:
4307:
4294:
4274:(4): 679–688.
4253:
4247:
4230:
4224:
4208:
4202:
4189:
4183:
4173:, ed. (2001).
4165:
4162:
4159:
4158:
4151:
4137:Storm Watchers
4125:
4071:
4036:
4003:
3994:|website=
3958:
3928:
3901:
3888:
3885:on 2012-02-06.
3867:10.1.1.423.508
3832:
3825:
3807:
3800:
3780:
3703:
3623:
3583:
3564:(2): 123–160.
3548:
3525:
3512:
3499:
3480:(4): 437–447.
3457:
3436:
3415:
3384:
3348:
3313:
3304:
3291:
3272:(400): 49–59.
3256:
3237:
3201:
3200:
3198:
3195:
3193:
3192:
3187:
3182:
3177:
3172:
3167:
3162:
3157:
3152:
3147:
3142:
3137:
3132:
3127:
3122:
3117:
3112:
3107:
3102:
3097:
3092:
3087:
3082:
3077:
3072:
3067:
3062:
3057:
3052:
3046:
3044:
3041:
3037:fluid dynamics
3033:chaotic nature
3024:
3021:
3002:
2999:
2993:
2990:
2981:Main article:
2978:
2975:
2973:
2970:
2969:
2968:
2963:
2954:
2952:Predictability
2949:
2947:Forecast error
2944:
2939:
2917:
2916:
2913:
2898:
2881:Starting with
2868:
2867:
2864:
2849:
2827:
2824:
2818:
2815:
2787:
2784:
2781:
2777:
2773:
2770:
2763:
2760:
2757:
2754:
2751:
2748:
2745:
2742:
2738:
2734:
2731:
2725:
2722:
2719:
2716:
2713:
2699:Forecast skill
2695:
2694:Other measures
2692:
2671:
2666:
2658:
2652:
2649:
2646:
2642:
2638:
2633:
2629:
2624:
2618:
2613:
2610:
2607:
2604:
2601:
2597:
2590:
2587:
2584:
2580:
2572:
2568:
2561:
2555:
2550:
2547:
2544:
2540:
2533:
2530:
2527:
2524:
2521:
2503:
2500:
2484:
2478:
2474:
2469:
2463:
2458:
2455:
2452:
2448:
2441:
2435:
2431:
2426:
2420:
2415:
2412:
2409:
2405:
2398:
2395:
2392:
2389:
2386:
2359:
2354:
2346:
2342:
2336:
2332:
2325:
2319:
2314:
2311:
2308:
2304:
2297:
2294:
2291:
2288:
2285:
2282:
2279:
2257:
2254:
2240:
2233:
2229:
2222:
2217:
2214:
2211:
2207:
2200:
2194:
2191:
2160:
2153:
2148:
2144:
2137:
2132:
2129:
2126:
2122:
2114:
2111:
2108:
2105:
2102:
2072:
2065:
2060:
2056:
2049:
2044:
2041:
2038:
2034:
2027:
2024:
2021:
2018:
2015:
2012:
2009:
2006:
2003:
1969:
1964:
1958:
1954:
1949:
1943:
1938:
1935:
1932:
1928:
1921:
1918:
1915:
1912:
1909:
1906:
1903:
1900:
1875:
1872:
1846:
1845:
1832:
1828:
1824:
1819:
1815:
1811:
1806:
1802:
1779:
1776:
1775:
1774:
1765:
1760:
1755:
1748:
1745:
1740:
1737:
1736:
1735:
1730:
1725:
1716:
1715:
1710:
1705:
1698:
1695:
1694:
1693:
1688:
1683:
1678:
1673:
1668:
1667:Cooke's method
1665:
1650:
1647:
1635:
1634:
1629:
1626:non-parametric
1599:
1596:
1595:
1594:
1589:
1584:
1578:
1573:
1567:
1566:
1563:
1556:
1555:
1549:
1543:
1538:
1533:
1531:Moving average
1520:
1517:
1500:
1497:
1494:
1491:
1488:
1485:
1482:
1479:
1476:
1465:
1464:
1447:
1441:
1438:
1433:
1429:
1424:
1421:
1416:
1412:
1407:
1404:
1399:
1396:
1393:
1389:
1385:
1384:
1381:
1378:
1373:
1369:
1364:
1361:
1358:
1353:
1349:
1345:
1340:
1336:
1332:
1329:
1324:
1321:
1318:
1314:
1310:
1309:
1306:
1301:
1300:
1275:
1271:
1248:
1244:
1231:
1230:
1215:
1210:
1205:
1202:
1198:
1193:
1188:
1185:
1181:
1173:
1168:
1163:
1159:
1155:
1152:
1149:
1145:
1139:
1136:
1131:
1127:
1123:
1118:
1114:
1110:
1109:
1094:
1091:
1075:
1071:
1067:
1064:
1061:
1058:
1055:
1035:
1015:
1004:
1003:
990:
987:
984:
981:
978:
975:
972:
969:
966:
963:
959:
955:
950:
946:
942:
939:
936:
929:
926:
899:
896:
893:
880:
877:
873:
872:
861:
857:
851:
848:
845:
838:
834:
830:
825:
821:
814:
810:
807:
802:
798:
794:
791:
786:
783:
780:
776:
772:
767:
763:
759:
754:
749:
746:
743:
739:
732:
729:
726:
722:
717:
712:
708:
704:
699:
695:
691:
688:
685:
678:
675:
648:
645:
642:
626:
623:
622:
621:
608:
604:
600:
595:
591:
587:
584:
581:
574:
571:
548:
547:Naïve approach
545:
526:
522:
518:
515:
512:
509:
506:
501:
497:
485:
484:
473:
469:
465:
460:
456:
452:
449:
446:
443:
440:
435:
431:
427:
424:
418:
415:
409:
404:
400:
396:
393:
390:
383:
380:
361:
358:
323:
320:
318:
315:
298:
295:
257:
254:
253:
252:
239:
230:
225:
220:
215:
210:
205:
200:
195:
189:credit ratings
178:
172:
167:
162:
157:
73:
70:
22:
13:
10:
9:
6:
4:
3:
2:
5571:
5570:
5559:
5556:
5554:
5551:
5549:
5546:
5544:
5541:
5539:
5536:
5535:
5533:
5519:
5516:
5514:
5511:
5509:
5506:
5504:
5501:
5497:
5491:
5488:
5486:
5483:
5481:
5478:
5476:
5473:
5471:
5468:
5467:
5463:
5458:
5455:Quantitative
5450:
5445:
5443:
5438:
5436:
5431:
5430:
5427:
5415:
5412:
5410:
5407:
5405:
5404:Delphi method
5402:
5400:
5397:
5396:
5393:
5388:
5380:
5375:
5373:
5368:
5366:
5361:
5360:
5357:
5347:
5346:
5341:
5335:
5329:
5326:
5324:
5321:
5319:
5316:
5314:
5313:Managerialism
5311:
5309:
5306:
5304:
5301:
5299:
5296:
5294:
5291:
5289:
5286:
5284:
5281:
5279:
5276:
5274:
5271:
5269:
5266:
5264:
5261:
5259:
5258:Collaboration
5256:
5254:
5251:
5250:
5248:
5244:
5238:
5235:
5233:
5230:
5228:
5225:
5223:
5220:
5219:
5217:
5213:
5207:
5204:
5202:
5199:
5197:
5194:
5192:
5189:
5187:
5184:
5183:
5181:
5177:
5171:
5168:
5166:
5163:
5161:
5160:Peter Drucker
5158:
5157:
5155:
5149:
5143:
5140:
5138:
5135:
5133:
5130:
5129:
5127:
5121:
5115:
5112:
5110:
5109:Team building
5107:
5105:
5102:
5100:
5097:
5095:
5092:
5090:
5087:
5085:
5082:
5080:
5077:
5075:
5072:
5070:
5067:
5065:
5062:
5060:
5057:
5055:
5052:
5050:
5047:
5045:
5042:
5041:
5039:
5033:
5027:
5024:
5022:
5019:
5017:
5014:
5013:
5011:
5007:
4997:
4994:
4992:
4989:
4987:
4984:
4982:
4979:
4977:
4974:
4972:
4969:
4967:
4964:
4962:
4959:
4957:
4954:
4952:
4949:
4947:
4944:
4943:
4941:
4939:
4935:
4929:
4926:
4924:
4921:
4919:
4916:
4915:
4913:
4909:
4903:
4900:
4898:
4895:
4893:
4890:
4888:
4885:
4883:
4880:
4878:
4875:
4874:
4872:
4866:
4856:
4853:
4851:
4848:
4846:
4843:
4842:
4840:
4838:
4834:
4828:
4825:
4821:
4818:
4816:
4813:
4812:
4811:
4807:
4804:
4802:
4799:
4798:
4796:
4794:
4790:
4787:
4779:
4769:
4766:
4762:
4759:
4758:
4757:
4754:
4750:
4747:
4745:
4742:
4741:
4740:
4737:
4735:
4732:
4731:
4729:
4725:
4719:
4716:
4714:
4711:
4709:
4706:
4704:
4701:
4699:
4696:
4694:
4691:
4689:
4688:Communication
4686:
4684:
4681:
4679:
4676:
4674:
4671:
4670:
4668:
4664:
4660:
4657:
4653:
4650:
4642:
4636:
4633:
4631:
4628:
4626:
4623:
4621:
4618:
4616:
4613:
4611:
4608:
4604:
4601:
4600:
4599:
4596:
4594:
4591:
4589:
4586:
4585:
4583:
4577:
4571:
4568:
4566:
4563:
4562:
4559:
4555:
4548:
4543:
4541:
4536:
4534:
4529:
4528:
4525:
4519:
4516:
4514:
4511:
4509:
4506:
4504:
4501:
4499:
4496:
4493:
4490:
4488:
4485:
4483:
4482:
4477:
4474:
4469:
4465:
4464:
4460:
4448:
4444:
4440:
4434:
4430:
4426:
4422:
4418:
4414:
4410:
4406:
4402:
4398:
4393:
4389:
4383:
4379:
4375:
4371:
4367:
4361:
4357:
4352:
4348:
4342:
4338:
4333:
4329:
4323:
4319:
4314:
4310:
4304:
4300:
4295:
4291:
4287:
4282:
4277:
4273:
4269:
4262:
4258:
4254:
4250:
4244:
4239:
4238:
4231:
4227:
4221:
4217:
4214:(June 1993).
4213:
4209:
4205:
4199:
4195:
4190:
4186:
4180:
4176:
4172:
4168:
4167:
4163:
4154:
4148:
4144:
4139:
4138:
4129:
4126:
4121:
4117:
4112:
4111:11250/2579292
4107:
4102:
4097:
4093:
4089:
4085:
4078:
4076:
4072:
4067:
4063:
4059:
4055:
4051:
4047:
4040:
4037:
4031:
4026:
4022:
4018:
4014:
4007:
4004:
3999:
3987:
3973:
3972:
3965:
3963:
3959:
3947:
3943:
3939:
3932:
3929:
3916:
3912:
3905:
3902:
3898:
3892:
3889:
3881:
3877:
3873:
3868:
3863:
3859:
3855:
3854:
3846:
3842:
3836:
3833:
3828:
3822:
3818:
3811:
3808:
3803:
3797:
3793:
3792:
3784:
3781:
3776:
3772:
3767:
3762:
3758:
3754:
3749:
3744:
3739:
3734:
3730:
3726:
3722:
3718:
3714:
3707:
3704:
3699:
3695:
3690:
3685:
3681:
3677:
3672:
3671:11311/1233353
3667:
3662:
3657:
3653:
3649:
3645:
3641:
3637:
3630:
3628:
3624:
3611:
3607:
3603:
3596:
3594:
3592:
3590:
3588:
3584:
3579:
3575:
3571:
3567:
3563:
3559:
3552:
3549:
3544:
3540:
3536:
3529:
3526:
3522:
3516:
3513:
3509:
3503:
3500:
3495:
3491:
3487:
3483:
3479:
3475:
3468:
3461:
3458:
3446:
3440:
3437:
3425:
3419:
3416:
3411:
3407:
3403:
3399:
3395:
3388:
3385:
3374:on 2010-06-20
3370:
3366:
3359:
3352:
3349:
3338:on 2012-07-11
3334:
3327:
3320:
3318:
3314:
3308:
3305:
3301:
3295:
3292:
3287:
3283:
3279:
3275:
3271:
3267:
3260:
3257:
3252:
3251:
3244:
3242:
3238:
3233:
3229:
3225:
3221:
3217:
3213:
3206:
3203:
3196:
3191:
3188:
3186:
3183:
3181:
3178:
3176:
3173:
3171:
3168:
3166:
3163:
3161:
3160:Spending wave
3158:
3156:
3153:
3151:
3148:
3146:
3143:
3141:
3138:
3136:
3133:
3131:
3130:Optimism bias
3128:
3126:
3123:
3121:
3120:Least squares
3118:
3116:
3113:
3111:
3108:
3106:
3103:
3101:
3098:
3096:
3093:
3091:
3088:
3086:
3083:
3081:
3078:
3076:
3073:
3071:
3068:
3066:
3063:
3061:
3058:
3056:
3053:
3051:
3048:
3047:
3042:
3040:
3038:
3034:
3030:
3029:Edward Lorenz
3022:
3020:
3016:
3013:
3009:
3000:
2998:
2991:
2989:
2984:
2976:
2971:
2967:
2964:
2962:
2959:, similar to
2958:
2955:
2953:
2950:
2948:
2945:
2943:
2940:
2938:
2935:
2934:
2933:
2932:
2928:
2926:
2922:
2914:
2911:
2907:
2903:
2899:
2896:
2892:
2888:
2884:
2880:
2879:
2878:
2876:
2871:
2865:
2862:
2858:
2854:
2850:
2847:
2843:
2842:
2841:
2839:
2834:
2832:
2825:
2823:
2816:
2814:
2810:
2808:
2803:
2785:
2782:
2779:
2775:
2771:
2768:
2761:
2758:
2755:
2752:
2749:
2746:
2743:
2740:
2736:
2732:
2729:
2723:
2720:
2717:
2714:
2711:
2700:
2693:
2691:
2689:
2684:
2669:
2650:
2647:
2644:
2640:
2636:
2631:
2627:
2616:
2611:
2608:
2605:
2602:
2599:
2595:
2588:
2585:
2582:
2578:
2570:
2566:
2553:
2548:
2545:
2542:
2538:
2531:
2528:
2525:
2522:
2519:
2511:
2507:
2502:Scaled errors
2501:
2499:
2476:
2472:
2461:
2456:
2453:
2450:
2446:
2433:
2429:
2418:
2413:
2410:
2407:
2403:
2396:
2393:
2390:
2387:
2384:
2372:
2357:
2344:
2340:
2334:
2330:
2317:
2312:
2309:
2306:
2302:
2295:
2292:
2289:
2286:
2283:
2280:
2277:
2266:
2262:
2255:
2253:
2238:
2231:
2227:
2220:
2215:
2212:
2209:
2205:
2198:
2189:
2174:
2158:
2151:
2146:
2142:
2135:
2130:
2127:
2124:
2120:
2112:
2109:
2106:
2103:
2100:
2089:
2085:
2070:
2063:
2058:
2054:
2047:
2042:
2039:
2036:
2032:
2025:
2022:
2019:
2016:
2013:
2010:
2007:
2004:
2001:
1990:
1986:
1982:
1967:
1956:
1952:
1941:
1936:
1933:
1930:
1926:
1919:
1916:
1913:
1910:
1907:
1904:
1901:
1898:
1887:
1883:
1879:
1873:
1871:
1868:
1866:
1861:
1858:
1854:
1849:
1830:
1826:
1822:
1817:
1813:
1809:
1804:
1800:
1789:
1788:
1787:
1785:
1777:
1773:
1769:
1766:
1764:
1761:
1759:
1756:
1754:
1751:
1750:
1747:Other methods
1746:
1744:
1738:
1734:
1731:
1729:
1726:
1724:
1721:
1720:
1719:
1714:
1711:
1709:
1706:
1704:
1701:
1700:
1696:
1692:
1689:
1687:
1684:
1682:
1679:
1677:
1674:
1672:
1671:Delphi method
1669:
1666:
1663:
1662:
1661:
1658:
1656:
1648:
1646:
1644:
1640:
1633:
1630:
1627:
1623:
1619:
1616:
1615:
1614:
1611:
1609:
1604:
1597:
1593:
1590:
1588:
1585:
1582:
1579:
1577:
1574:
1572:
1571:Extrapolation
1569:
1568:
1564:
1562:
1558:
1557:
1553:
1550:
1547:
1544:
1542:
1539:
1537:
1534:
1532:
1529:
1528:
1527:
1525:
1518:
1516:
1512:
1498:
1495:
1492:
1489:
1486:
1483:
1480:
1477:
1474:
1439:
1436:
1431:
1427:
1422:
1419:
1414:
1410:
1405:
1402:
1397:
1394:
1391:
1387:
1379:
1376:
1371:
1367:
1362:
1359:
1351:
1347:
1338:
1334:
1330:
1327:
1322:
1319:
1316:
1312:
1304:
1291:
1290:
1289:
1273:
1269:
1246:
1242:
1213:
1203:
1200:
1196:
1186:
1183:
1179:
1166:
1161:
1157:
1153:
1150:
1143:
1137:
1129:
1125:
1116:
1112:
1100:
1099:
1098:
1092:
1090:
1087:
1073:
1069:
1062:
1059:
1056:
1033:
1013:
985:
982:
979:
973:
970:
967:
964:
961:
957:
953:
948:
940:
937:
934:
924:
913:
912:
911:
897:
894:
891:
878:
876:
859:
855:
849:
846:
843:
836:
832:
828:
823:
819:
812:
808:
805:
800:
796:
792:
784:
781:
778:
774:
770:
765:
761:
752:
747:
744:
741:
737:
730:
727:
724:
720:
715:
710:
706:
702:
697:
689:
686:
683:
673:
662:
661:
660:
646:
643:
640:
632:
624:
606:
602:
598:
593:
585:
582:
579:
569:
558:
557:
556:
554:
546:
544:
540:
524:
520:
516:
513:
510:
507:
504:
499:
495:
471:
467:
458:
454:
450:
447:
444:
441:
438:
433:
429:
422:
413:
407:
402:
394:
391:
388:
378:
367:
366:
365:
359:
357:
354:
350:
346:
341:
336:
334:
330:
329:Delphi method
321:
316:
314:
312:
311:Du Pont model
308:
304:
296:
294:
291:
286:
283:
279:
276:
272:
271:
266:
261:
255:
251:
247:
243:
240:
238:
234:
231:
229:
226:
224:
221:
219:
216:
214:
211:
209:
206:
204:
201:
199:
196:
194:
193:credit scores
190:
186:
182:
179:
176:
173:
171:
168:
166:
163:
161:
158:
155:
154:profit margin
151:
147:
144:
143:
142:
139:
136:
132:
128:
123:
119:
117:
113:
109:
104:
102:
98:
93:
91:
87:
83:
78:
71:
69:
66:
62:
58:
56:
52:
48:
44:
40:
36:
32:
28:
19:
5456:
5386:
5385:Qualitative
5343:
5136:
4897:Supply chain
4870:relationship
4868:On aspect or
4761:Construction
4727:On component
4648:organization
4620:Intelligence
4480:
4428:
4400:
4396:
4377:
4355:
4336:
4317:
4298:
4271:
4267:
4236:
4215:
4193:
4174:
4136:
4128:
4091:
4087:
4049:
4045:
4039:
4020:
4016:
4006:
3975:. Retrieved
3970:
3950:. Retrieved
3941:
3931:
3919:. Retrieved
3914:
3904:
3891:
3880:the original
3857:
3851:
3835:
3816:
3810:
3790:
3783:
3720:
3716:
3706:
3646:(1): 19843.
3643:
3639:
3614:. Retrieved
3605:
3561:
3557:
3551:
3534:
3528:
3515:
3502:
3477:
3473:
3460:
3449:. Retrieved
3439:
3428:. Retrieved
3418:
3401:
3397:
3387:
3376:. Retrieved
3369:the original
3364:
3351:
3340:. Retrieved
3333:the original
3307:
3294:
3269:
3265:
3259:
3249:
3218:(2): 81–96.
3215:
3211:
3205:
3060:Cliodynamics
3026:
3017:
3004:
2995:
2986:
2930:
2929:
2924:
2920:
2918:
2909:
2905:
2901:
2894:
2890:
2886:
2882:
2874:
2872:
2869:
2860:
2856:
2852:
2845:
2835:
2829:
2820:
2811:
2804:
2697:
2687:
2685:
2508:
2505:
2373:
2263:
2259:
2175:
2086:
1983:
1880:
1877:
1869:
1864:
1862:
1857:correlations
1853:uncorrelated
1852:
1850:
1847:
1781:
1742:
1717:
1659:
1652:
1636:
1612:
1605:
1601:
1522:
1513:
1466:
1232:
1096:
1088:
1005:
882:
874:
659:is given by
628:
625:Drift method
550:
541:
486:
363:
337:
325:
300:
287:
280:
274:
268:
262:
259:
140:
134:
130:
124:
120:
106:Forecasting
105:
94:
79:
75:
72:Applications
59:
47:longitudinal
26:
25:
5558:Time series
5538:Forecasting
5457:forecasting
5387:forecasting
5137:Forecasting
5054:Distributed
4961:Information
4938:On resource
4882:Engineering
4708:Performance
4666:(top-level)
4593:Association
3723:(1): 1693.
3404:: 111–116.
3180:Time series
3001:Limitations
2983:Seasonality
2977:Seasonality
2855:= 1,2,...,
1723:Data mining
1655:probability
1628:techniques.
1561:Box–Jenkins
1524:Time series
250:meteorology
237:forecasting
65:uncertainty
39:time series
27:Forecasting
5532:Categories
5142:Leadership
5125:activities
5037:approaches
4991:Technology
4911:On problem
4892:Perception
4845:Accounting
4810:production
4806:Operations
4783:department
4698:Innovation
4673:Capability
4635:Reputation
4615:Healthcare
4603:Restaurant
4554:Management
4473:Prediction
4023:(3): 343.
3977:2016-05-14
3952:2022-12-06
3608:. OTexts.
3451:2012-08-28
3430:2012-08-28
3378:2011-12-29
3365:Interfaces
3342:2012-01-23
3197:References
3140:Prediction
3110:Futurology
1758:Simulation
1622:parametric
1608:algorithms
35:Prediction
5179:Education
5151:Pioneers,
5044:Adhocracy
5009:Positions
4981:Materials
4971:Knowledge
4887:Logistics
4801:Marketing
4693:Financial
4663:Strategic
4646:within an
4644:By focus,
4276:CiteSeerX
4120:2214-6296
4094:: 36–40.
4052:: 75–84.
3996:ignored (
3986:cite book
3862:CiteSeerX
3860:: 69–80.
3757:2045-2322
3680:2045-2322
3578:157150897
3232:157962452
2724:−
2648:−
2637:−
2596:∑
2586:−
2539:∑
2447:∑
2404:∑
2303:∑
2296:∗
2206:∑
2193:¯
2121:∑
2033:∑
1987:(MSE) or
1927:∑
1884:(MAE) or
1865:zero mean
1823:−
1499:η
1493:μ
1487:β
1481:γ
1475:α
1440:η
1423:μ
1420:−
1406:β
1380:δ
1363:γ
1331:α
1204:∈
1187:∈
1060:−
971:−
928:^
847:−
829:−
782:−
771:−
738:∑
728:−
677:^
573:^
417:¯
382:^
347:, simple
288:Finally,
51:hydrology
5153:scholars
5035:Methods,
4918:Conflict
4734:Facility
4655:On scope
4625:Military
4598:Business
4588:Academic
4376:(1998).
4066:73325253
3946:Archived
3921:16 March
3917:. OTexts
3775:35105929
3698:36400910
3616:16 March
3610:Archived
3494:16462529
3135:Planning
3043:See also
2931:See also
2904:= 2,...,
2512:(MASE):
2267:(MAPE):
2090:(RMSE):
1991:(MSPE):
1784:residual
290:futarchy
127:planning
31:estimate
18:Forecast
5459:methods
5389:methods
5215:Degrees
5123:Skills,
5016:Interim
4855:Records
4820:Quality
4815:Process
4785:managed
4768:Program
4756:Project
4739:Product
4718:Systems
4678:Capital
4579:By type
4405:Bibcode
4164:Sources
4143:222–224
3942:Hackage
3766:8807815
3725:Bibcode
3689:9674651
3648:Bibcode
3410:1596623
3286:2234183
3035:of the
2921:k+i -1)
1888:(MAD):
282:Betting
185:default
181:Finance
5026:Senior
5021:Middle
4986:Skills
4928:Stress
4923:Crisis
4902:Talent
4850:Office
4683:Change
4630:Public
4453:
4435:
4384:
4362:
4343:
4324:
4305:
4278:
4245:
4222:
4200:
4181:
4149:
4118:
4064:
3864:
3823:
3798:
3773:
3763:
3755:
3696:
3686:
3678:
3576:
3492:
3408:
3284:
3230:
2908:where
2859:where
2709:
2701:(SS):
2686:where
2382:
2275:
2184:
2098:
1999:
1896:
1797:
1467:where
1006:where
487:where
340:models
135:should
55:future
5246:Other
4837:Staff
4827:Sales
4749:Brand
4703:Legal
4610:Court
4264:(PDF)
4062:S2CID
3883:(PDF)
3848:(PDF)
3574:S2CID
3490:S2CID
3470:(PDF)
3424:"FAQ"
3372:(PDF)
3361:(PDF)
3336:(PDF)
3329:(PDF)
3282:JSTOR
3228:S2CID
3008:stock
2887:k + i
1559:e.g.
1288:are
631:drift
112:chart
4996:Time
4976:Land
4793:Line
4713:Risk
4433:ISBN
4382:ISBN
4360:ISBN
4341:ISBN
4322:ISBN
4303:ISBN
4243:ISBN
4220:ISBN
4198:ISBN
4179:ISBN
4147:ISBN
4116:ISSN
3998:help
3923:2018
3821:ISBN
3796:ISBN
3771:PMID
3753:ISSN
3694:PMID
3676:ISSN
3618:2018
3406:SSRN
3010:and
2836:For
1770:and
1643:GMDH
553:data
353:GMDH
275:i.e.
248:and
235:and
191:and
187:via
148:and
131:will
114:and
63:and
61:Risk
4413:doi
4286:doi
4106:hdl
4096:doi
4054:doi
4025:doi
3872:doi
3761:PMC
3743:hdl
3733:doi
3684:PMC
3666:hdl
3656:doi
3566:doi
3539:doi
3482:doi
3274:doi
3270:100
3220:doi
2906:T–k
2895:k+i
2891:k+i
2293:100
910:is
267:'s
263:In
45:or
5534::
4411:.
4401:15
4399:.
4284:.
4272:22
4270:.
4266:.
4145:.
4114:.
4104:.
4092:49
4090:.
4086:.
4074:^
4060:.
4048:.
4021:51
4019:.
4015:.
3990::
3988:}}
3984:{{
3961:^
3940:.
3913:.
3870:.
3856:.
3850:.
3769:.
3759:.
3751:.
3741:.
3731:.
3721:12
3719:.
3715:.
3692:.
3682:.
3674:.
3664:.
3654:.
3644:12
3642:.
3638:.
3626:^
3604:.
3586:^
3572:.
3562:23
3560:.
3488:.
3476:.
3472:.
3402:39
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