Time series analysis serves as a practical way to investigate data that changes over time, and has great potential for development in fields such as weather prediction and financial engineering. However, due to the imperfections in technology, it is not always possible to obtain precise observational data. Therefore, modeling with uncertain time series is more suitable. Choosing appropriate parameter estimation methods is a critical aspect of the modeling process for uncertain time series. This paper proposes using maximum likelihood estimation for the parameter estimation of the first-order uncertain moving average (UMA) model, and for predicting future values and calculating the confidence intervals. Subsequently, the effectiveness of this method is demonstrated through numerical examples. Firstly, we employ an iterative method to convert the first-order UMA model into an uncertain autoregressive (UAR) model. Secondly, the maximum likelihood method is used to estimate the unknown parameters of the UMA model. Additionally, for this model where the observations are linear uncertain variables, a specific maximum likelihood estimation approach is provided. Thirdly, following the estimation values obtained, future data predictions and confidence intervals are calculated. Furthermore, when the observations are linear uncertain variables, corresponding confidence intervals are also provided. Finally, two practical cases are presented to demonstrate the practicality of the method. Moreover, contrasted with the least squares method, the results indicate that this method can enhance the accuracy of predictions.
| Published in | Mathematics and Computer Science (Volume 10, Issue 4) |
| DOI | 10.11648/j.mcs.20251004.12 |
| Page(s) | 70-82 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
| Copyright |
Copyright © The Author(s), 2025. Published by Science Publishing Group |
Uncertainty Theory, Uncertain Time Series Analysis, Uncertain Moving Average Model, Maximum Likelihood Estimation
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APA Style
Wang, X., He, B. (2025). Maximum Likelihood Estimation for Uncertain Moving Average Model Under Imprecise Observations. Mathematics and Computer Science, 10(4), 70-82. https://doi.org/10.11648/j.mcs.20251004.12
ACS Style
Wang, X.; He, B. Maximum Likelihood Estimation for Uncertain Moving Average Model Under Imprecise Observations. Math. Comput. Sci. 2025, 10(4), 70-82. doi: 10.11648/j.mcs.20251004.12
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Download@article{10.11648/j.mcs.20251004.12,
author = {Xiaosheng Wang and Ben He},
title = {Maximum Likelihood Estimation for Uncertain Moving Average Model Under Imprecise Observations
},
journal = {Mathematics and Computer Science},
volume = {10},
number = {4},
pages = {70-82},
doi = {10.11648/j.mcs.20251004.12},
url = {https://doi.org/10.11648/j.mcs.20251004.12},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.mcs.20251004.12},
abstract = {Time series analysis serves as a practical way to investigate data that changes over time, and has great potential for development in fields such as weather prediction and financial engineering. However, due to the imperfections in technology, it is not always possible to obtain precise observational data. Therefore, modeling with uncertain time series is more suitable. Choosing appropriate parameter estimation methods is a critical aspect of the modeling process for uncertain time series. This paper proposes using maximum likelihood estimation for the parameter estimation of the first-order uncertain moving average (UMA) model, and for predicting future values and calculating the confidence intervals. Subsequently, the effectiveness of this method is demonstrated through numerical examples. Firstly, we employ an iterative method to convert the first-order UMA model into an uncertain autoregressive (UAR) model. Secondly, the maximum likelihood method is used to estimate the unknown parameters of the UMA model. Additionally, for this model where the observations are linear uncertain variables, a specific maximum likelihood estimation approach is provided. Thirdly, following the estimation values obtained, future data predictions and confidence intervals are calculated. Furthermore, when the observations are linear uncertain variables, corresponding confidence intervals are also provided. Finally, two practical cases are presented to demonstrate the practicality of the method. Moreover, contrasted with the least squares method, the results indicate that this method can enhance the accuracy of predictions.
},
year = {2025}
}
TY - JOUR T1 - Maximum Likelihood Estimation for Uncertain Moving Average Model Under Imprecise Observations AU - Xiaosheng Wang AU - Ben He Y1 - 2025/09/25 PY - 2025 N1 - https://doi.org/10.11648/j.mcs.20251004.12 DO - 10.11648/j.mcs.20251004.12 T2 - Mathematics and Computer Science JF - Mathematics and Computer Science JO - Mathematics and Computer Science SP - 70 EP - 82 PB - Science Publishing Group SN - 2575-6028 UR - https://doi.org/10.11648/j.mcs.20251004.12 AB - Time series analysis serves as a practical way to investigate data that changes over time, and has great potential for development in fields such as weather prediction and financial engineering. However, due to the imperfections in technology, it is not always possible to obtain precise observational data. Therefore, modeling with uncertain time series is more suitable. Choosing appropriate parameter estimation methods is a critical aspect of the modeling process for uncertain time series. This paper proposes using maximum likelihood estimation for the parameter estimation of the first-order uncertain moving average (UMA) model, and for predicting future values and calculating the confidence intervals. Subsequently, the effectiveness of this method is demonstrated through numerical examples. Firstly, we employ an iterative method to convert the first-order UMA model into an uncertain autoregressive (UAR) model. Secondly, the maximum likelihood method is used to estimate the unknown parameters of the UMA model. Additionally, for this model where the observations are linear uncertain variables, a specific maximum likelihood estimation approach is provided. Thirdly, following the estimation values obtained, future data predictions and confidence intervals are calculated. Furthermore, when the observations are linear uncertain variables, corresponding confidence intervals are also provided. Finally, two practical cases are presented to demonstrate the practicality of the method. Moreover, contrasted with the least squares method, the results indicate that this method can enhance the accuracy of predictions. VL - 10 IS - 4 ER -
School of Mathematics and Physics, Hebei University of Engineering, Handan, China
School of Mathematics and Physics, Hebei University of Engineering, Handan, China
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