A continuous-time analog of the Martingale model of forecast evolution
In many practical situations, a manager would like to simulate forecasts for periods whose duration (e.g., week) is not equal to the periods (e.g., month) for which past forecasting data are available. This article addresses this problem by developing a continuous-time analog of the Martingale model...
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| Published in: | IIE transactions Vol. 46; no. 1; pp. 23 - 34 |
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| Main Authors: | , |
| Format: | Journal Article |
| Language: | English |
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Taylor & Francis Group
02-01-2014
Taylor & Francis Ltd |
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| Abstract | In many practical situations, a manager would like to simulate forecasts for periods whose duration (e.g., week) is not equal to the periods (e.g., month) for which past forecasting data are available. This article addresses this problem by developing a continuous-time analog of the Martingale model of forecast evolution, called the Continuous-Time Martingale Model of Forecast Evolution (CTMMFE). The CTMMFE is used to parameterize the variance-covariance matrix of forecast updates in such a way that the matrix can be scaled for any planning period length. The parameters can then be estimated from past forecasting data corresponding to a specific planning period. Once the parameters are estimated, a variance-covariance matrix can be generated for any planning period length. Numerical experiments are conducted to derive insights into how various characteristics of the variance-covariance matrix (for example, the underlying correlation structure) influence the number of parameters needed as well as the accuracy of the approximation. |
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| AbstractList | In many practical situations, a manager would like to simulate forecasts for periods whose duration (e.g., week) is not equal to the periods (e.g., month) for which past forecasting data are available. This article addresses this problem by developing a continuous-time analog of the Martingale model of forecast evolution, called the Continuous-Time Martingale Model of Forecast Evolution (CTMMFE). The CTMMFE is used to parameterize the variance-covariance matrix of forecast updates in such a way that the matrix can be scaled for any planning period length. The parameters can then be estimated from past forecasting data corresponding to a specific planning period. Once the parameters are estimated, a variance-covariance matrix can be generated for any planning period length. Numerical experiments are conducted to derive insights into how various characteristics of the variance-covariance matrix (for example, the underlying correlation structure) influence the number of parameters needed as well as the accuracy of the approximation. In many practical situations, a manager would like to simulate forecasts for periods whose duration (e.g., week) is not equal to the periods (e.g., month) for which past forecasting data are available. This article addresses this problem by developing a continuous-time analog of the Martingale model of forecast evolution, called the Continuous-Time Martingale Model of Forecast Evolution (CTMMFE). The CTMMFE is used to parameterize the variance-covariance matrix of forecast updates in such a way that the matrix can be scaled for any planning period length. The parameters can then be estimated from past forecasting data corresponding to a specific planning period. Once the parameters are estimated, a variance-covariance matrix can be generated for any planning period length. Numerical experiments are conducted to derive insights into how various characteristics of the variance-covariance matrix (for example, the underlying correlation structure) influence the number of parameters needed as well as the accuracy of the approximation. [PUBLICATION ABSTRACT] In many practical situations, a manager would like to simulate forecasts for periods whose duration (e.g., week) is not equal to the periods (e.g., month) for which past forecasting data are available. This article addresses this problem by developing a continuous-time analog of the Martingale model of forecast evolution, called the Continuous-Time Martingale Model of Forecast Evolution (CTMMFE). The CTMMFE is used to parameterize the varianceacovariance matrix of forecast updates in such a way that the matrix can be scaled for any planning period length. The parameters can then be estimated from past forecasting data corresponding to a specific planning period. Once the parameters are estimated, a varianceacovariance matrix can be generated for any planning period length. Numerical experiments are conducted to derive insights into how various characteristics of the varianceacovariance matrix (for example, the underlying correlation structure) influence the number of parameters needed as well as the accuracy of the approximation. |
| Author | Sapra, Amar Jackson, Peter L. |
| Author_xml | – sequence: 1 givenname: Amar surname: Sapra fullname: Sapra, Amar organization: Indian Institute of Management Bangalore – sequence: 2 givenname: Peter L. surname: Jackson fullname: Jackson, Peter L. organization: School of Operations Research and Industrial Engineering , Cornell University |
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| Cites_doi | 10.1287/msom.1080.0245 10.1016/j.ijpe.2010.11.005 10.1287/mnsc.18.7.370 10.1287/mnsc.1120.1581 10.1287/opre.51.6.969.24920 10.1007/978-1-4612-0949-2 10.1287/msom.1060.0116 10.1080/07408179408966604 10.1002/(SICI)1520-6750(199603)43:2<289::AID-NAV8>3.0.CO;2-6 10.1287/mnsc.47.9.1268.9787 10.1287/mnsc.16.2.B93 10.1080/07408170600967131 10.1287/mnsc.47.10.1326.10260 10.1287/opre.1060.0338 10.1007/978-3-642-51693-1_2 |
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| SubjectTerms | Approximation forecast evolution Forecasting Forecasting techniques Game theory Martingale Mathematical problems Parameter estimation Stochastic models Studies |
| Title | A continuous-time analog of the Martingale model of forecast evolution |
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