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Ridge estimation of uncertain vector autoregressive model with imprecise data

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Abstract

Uncertain vector autoregressive model (UVAR) is used to describe the variational relationship between multivariable time series. Based on the imprecise observations, the issue of predicting the future data accurately attracts more and more scholars attentions. This paper takes the ridge estimation into consideration and applies it into uncertain vector autoregressive model. In order to determine the shrinkage parameter, we use the cross-validation to solve this problem. On this basis, we conduct the residual analysis. A point estimation and a confidence interval are given to predict the future value. Finally, two numerical examples are applyied to clarify the feasibility and validity of the ridge estimation, compared with the least square estimation.

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References

  • Chen D, Yang X (2021) Ridge estimation for uncertain autoregressive model with imprecise observations. Int J Uncertain Fuzziness Knowl Based Syst 29(1):37–55

    Article  MathSciNet  Google Scholar 

  • Chen D, Yang X (2021) Maximum likelihood estimation for uncertain autoregressive model with application to carbon dioxide emissions. J Intell Fuzzy Syst 40(1):1391–1399

    Article  Google Scholar 

  • Gao X, Xue C (2022) Ridge Estimation for Uncertain Moving Average Model Under Imprecise Observations. Int J Uncertain Fuzziness Knowl Based Syst 30(02):171–187

    Article  MathSciNet  Google Scholar 

  • Li H, Yang X (2021) Smoothly clipped absolute deviation estimation for uncertain autoregressive model. J Intell Fuzzy Syst 40(6):11875–11885

    Article  Google Scholar 

  • Liu B (2007) Uncertainty theory, 2nd edn. Springer, Berlin

    Google Scholar 

  • Liu Z (2021) Huber estimation for uncertain autoregressive model. J Uncertain Syst 14(02):2150010

    Article  Google Scholar 

  • Liu Z, Yang X (2022) Cross validation for uncertain autoregressive model. Commun Stat-Simul Comput 51(8):4715–4726

    Article  MathSciNet  Google Scholar 

  • Shi Y, Sheng Y (2023) Uncertain vector autoregressive smoothly moving average model. Commun Stat-Simul Comput 1–12. https://doi.org/10.1080/03610918.2023.2213419

  • Tang H (2020) Uncertain vector autoregressive model with imprecise observations. Soft Comput 24(22):17001–17007. https://doi.org/10.1007/s00500-020-04991-9

    Article  Google Scholar 

  • Tang H (2022) Uncertain threshold autoregressive model with imprecise observations. Commun Stat Theory Methods 51(24):8776–8785

    Article  MathSciNet  Google Scholar 

  • Tang H, Dalin (2021) Uncertain max-autoregressive model with imprecise observations. J Intell Fuzzy Syst 41(6): 6915-6922

  • Walker GT (1931) On periodicity in series of related terms. Proc R Soc Lond Ser A, Containing Papers of a Mathematical and Physical Character 131(818): 518–532

  • Xin Y, Yang X, Gao J (2021) Least squares estimation for the high-order uncertain moving average model with application to carbon dioxide emissions. Int J Gen Syst 50(6):724–740

    Article  MathSciNet  Google Scholar 

  • Xin Y, Gao J, Yang X et al (2023) Maximum likelihood estimation for uncertain autoregressive moving average model with application in financial market. J Comput Appl Math 417:114604

    Article  MathSciNet  Google Scholar 

  • Yang X, Liu B (2019) Uncertain time series analysis with imprecise observations. Fuzzy Optim Decis Making 18(3):263–278

    Article  MathSciNet  Google Scholar 

  • Yang X, Ni Y (2021) Least-squares estimation for uncertain moving average model. Commun Stat-Theory Methods 50(17):4134–4143

    Article  MathSciNet  Google Scholar 

  • Yang X, Park GK, Hu Y (2020) Least absolute deviations estimation for uncertain autoregressive model. Soft Comput 24:18211–18217

    Article  Google Scholar 

  • Yule GU (1927) On a method of investigating periodicities in disturbed series with special reference to Wolfer’s sunspot numbers. Philos Trans R Soc Lond 226:267–298

    Article  Google Scholar 

  • Zhang Z, Yang X, Gao J (2020) Uncertain autoregressive model via LASSO procedure. Int J Uncertain Fuzziness Knowl Based Syst 28(06):939–956

    Article  MathSciNet  Google Scholar 

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Acknowledgements

This work was funded by the Key Research and Development Plan Project of Xinjiang Uygur Autonomous Region (Grant No. 2021B03003-1) and the National Natural Science Foundation of China (Grant No. 12061072).

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Authors and Affiliations

  1. College of Mathematics and System Science, Xinjiang University, Urumqi, 830046, China

    Yuxin Shi & Yuhong Sheng

  2. Center for Disease Control and Prevention of Xinjiang Uygur Autonomous Region, Urumqi, 830002, People’s Republic of China

    Ling Zhang

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  1. Yuxin Shi
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  2. Ling Zhang
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  3. Yuhong Sheng
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Correspondence to Yuhong Sheng.

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Shi, Y., Zhang, L. & Sheng, Y. Ridge estimation of uncertain vector autoregressive model with imprecise data. J Ambient Intell Human Comput 15, 2143–2152 (2024). https://doi.org/10.1007/s12652-023-04743-1

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  • DOI: https://doi.org/10.1007/s12652-023-04743-1

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