Confidence intervals

Makridakis, Spyros; Hibon, Michèle; Lusk, Ed; Belhadjali, Moncef

doi:10.1016/0169-2070(87)90045-8

Cited by 77 publications

(12 citation statements)

References 10 publications

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“…The original errors from these forecasts proved to be asymmetric. For the six-year-ahead extrapolation forecasts using Holt's exponential smoothing, 33.1% of the actual values fell above the upper 95% limits, while 8.8% fell below the lower 95% limits (see Exhibits 3 and 4 in Makridakis et al 1987). The results were similar for other extrapolation methods they tested.…”

Section: Assessing Uncertaintysupporting

confidence: 71%

“…In particular, they tend to be too narrow for ex ante time series forecasts (i.e., too many actual observations fall outside the specified intervals). As Makridakis et al (1987) show, this problem occurs for a wide range of economic and demographic data. It is more serious for annual than for quarterly data, and more so for quarterly than monthly data.…”

Section: Assessing Uncertaintymentioning

confidence: 99%

“…In the M-competition (Makridakis et al 1987), academic researchers used additive extrapolation models. The original errors from these forecasts proved to be asymmetric.…”

Section: Assessing Uncertaintymentioning

confidence: 99%

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Extrapolation for Time-Series and Cross-Sectional Data

Armstrong

2001

International Series in Operations Research &Amp; Management Science

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Extrapolation methods are reliable, objective, inexpensive, quick, and easily automated. As a result, they are widely used, especially for inventory and production forecasts, for operational planning for up to two years ahead, and for long-term forecasts in some situations, such as population forecasting. This paper provides principles for selecting and preparing data, making seasonal adjustments, extrapolating, assessing uncertainty, and identifying when to use extrapolation. The principles are based on received wisdom (i.e., experts' commonly held opinions) and on empirical studies. Some of the more important principles are:• In selecting and preparing data, use all relevant data and adjust the data for important events that occurred in the past.• Make seasonal adjustments only when seasonal effects are expected and only if there is good evidence by which to measure them.• In extrapolating, use simple functional forms. Weight the most recent data heavily if there are small measurement errors, stable series, and short forecast horizons. Domain knowledge and forecasting expertise can help to select effective extrapolation procedures. When there is uncertainty, be conservative in forecasting trends. Update extrapolation models as new data are received.• To assess uncertainty, make empirical estimates to establish prediction intervals.• Use pure extrapolation when many forecasts are required, little is known about the situation, the situation is stable, and expert forecasts might be biased. Disciplines Business | Marketing ABSTRACTExtrapolation methods are reliable, objective, inexpensive, quick, and easily automated. As a result, they are widely used, especially for inventory and production forecasts, for operational planning for up to two years ahead, and for long-term forecasts in some situations, such as population forecasting. This paper provides principles for selecting and preparing data, making seasonal adjustments, extrapolating, assessing uncertainty, and identifying when to use extrapolation. The principles are based on received wisdom (i.e., experts' commonly held opinions) and on empirical studies. Some of the more important principles are:

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Section: Assessing Uncertaintysupporting

confidence: 71%

Section: Assessing Uncertaintymentioning

confidence: 99%

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Extrapolation for Time-Series and Cross-Sectional Data

Armstrong

2001

International Series in Operations Research &Amp; Management Science

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“…Thissen et al (2003) examine one long time series from the ARMA family, while Zhang (2001) examine 8 stochastic processes from the ARMA family and 30 simulated time series for each stochastic process. The forecasting methods are ARMA models, NN and SVM in the former study and ARMA models and NN in the latter study, while Makridakis and Hibon (1987), Makridakis and Hibon (2000) and Ahmed et al (2010) do not focus their comparisons on the stochastic-ML dipole.…”

Section: The Broader Perspectivementioning

confidence: 99%

Comparison of Stochastic and Machine Learning Methods for Multi-Step Ahead Forecasting of Hydrological Processes

Papacharalampous¹,

Tyralis²,

Koutsoyiannis³

2017

Preprint

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Abstract:We perform an extensive comparison between 11 stochastic to 9 machine learning methods regarding their multi-step ahead forecasting properties by conducting 12 large-scale computational experiments. Each of these experiments uses 2 000 time series generated by linear stationary stochastic processes. We conduct each simulation experiment twice; the first time using time series of 110 values and the second time using time series of 310 values. Additionally, we conduct 92 real-world case studies using mean monthly time series of streamflow and particularly focus on one of them to reinforce the findings and highlight important facts. We quantify the performance of the methods using 18 metrics. The results indicate that the machine learning methods do not differ dramatically from the stochastic, while none of the methods under comparison is uniformly better or worse than the rest. However, there are methods that are regularly better or worse than others according to specific metrics.

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“…In the M-Competition (Makridakis et al, 1987), leading academic researchers used additive extrapolation models whose forecast errors proved to be asymmetric. For six-year-ahead extrapolation forecasts using Holt's exponential smoothing, 33.1% of the actual values fell above the upper 95% limits, while 8.8% fell below the lower 95% limits (see Exhibits 3 and 4 in Makridakis et al, 1987).…”

mentioning

confidence: 99%

Identification of asymmetric prediction intervals through causal forces

Armstrong

Collopy

2001

Journal of Forecasting

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When causal forces are specified, the expected direction of the trend can be compared with the trend based on extrapolation. Series in which the expected trend conflicts with the extrapolated trend are called contrary series. We hypothesized that contrary series would have asymmetric forecast errors, with larger errors in the direction of the expected trend. Using annual series that contained minimal information about causality, we examined 671 contrary forecasts. As expected, most (81%) of the errors were in the direction of the causal forces. Also as expected, the asymmetries were more likely for longer forecast horizons; for six-year-ahead forecasts, 89% of the forecasts were in the expected direction. The asymmetries were often substantial. Contrary series should be flagged and treated separately when prediction intervals are estimated, perhaps by shifting the interval in the direction of the causal forces. Identification of Asymmetric Prediction Intervals through Causal Forces J. Scott ArmstrongThe Wharton School, University of Pennsylvania Fred CollopyWeatherhead School of Management, Case Western Reserve University Abstract When causal forces are specified, the expected direction of the trend can be compared with the trend based on extrapolation. Series in which the expected trend conflicts with the extrapolated trend are called contrary series. We hypothesized that contrary series would have asymmetric forecast errors, with larger errors in the direction of the expected trend. Using annual series that contained minimal information about causality, we examined 671 contrary forecasts. As expected, most (81%) of the errors were in the direction of the causal forces. Also as expected, the asymmetries were more likely for longer forecast horizons; for six-year-ahead forecasts, 89% of the forecasts were in the expected direction. The asymmetries were often substantial. Contrary series should be flagged and treated separately when prediction intervals are estimated, perhaps by shifting the interval in the direction of the causal forces.

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Confidence intervals

Cited by 77 publications

References 10 publications

Extrapolation for Time-Series and Cross-Sectional Data

Extrapolation for Time-Series and Cross-Sectional Data

Comparison of Stochastic and Machine Learning Methods for Multi-Step Ahead Forecasting of Hydrological Processes

Identification of asymmetric prediction intervals through causal forces

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