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Journal of Statistical Theory and Practice

, Volume 12, Issue 2, pp 356–369 | Cite as

A note on autoregressive models with fuzzy random variables

  • Dabuxilatu Wang
Article
  • 1 Downloads

Abstract

In this note, we propose some novel autoregressive models with fuzzy random variables, and by which the definitions and proofs for the AR(p) model given in a paper by Wang are improved. We also demonstrate some mistakes in an example of the AR sequence given in a paper by Feng et al. and correct these. Finally, a practical example on forecasting of the Hang Seng Index (HSI) is presented for an explanation of the proposed models.

Keywords

Fuzzy random variables autoregressive models time series 

AMS Subject Classification

62F86 52A22 

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References

  1. Brockwell, P. J., and R. A. Davis. 1991. Time series: Theory and methods, 2nd ed. New York, NY: Springer-Verlag.CrossRefGoogle Scholar
  2. Diamond, P., and P. Kloeden. 1994. Metric spaces of fuzzy sets. Hong Kong: World Scientific.zbMATHGoogle Scholar
  3. Feng, Y. 1999. Mean-square integral and differential of fuzzy stochastic prosses. Fuzzy Sets and Systems 102:271–80.MathSciNetCrossRefGoogle Scholar
  4. Feng, Y., L. Hu, and H. Shu. 2001. The variance and covariance of fuzzy random variables and their applications. Fuzzy Sets and Systems 120:487–97.MathSciNetCrossRefGoogle Scholar
  5. Gil, M., M. López-Diaz, and D. A. Ralescu. 2006. Overview on the development of fuzzy random variables. Fuzzy Sets and Systems 157:2546–57.MathSciNetCrossRefGoogle Scholar
  6. González-Rodríguez, G., Á. Blanco, A. Colubi, and M. A. Lubiano. 2009. Estimation of a linear regression model for fuzzy random variables. Fuzzy Sets and Systems 160:357–70.MathSciNetCrossRefGoogle Scholar
  7. Krätschmer, V. 2004. Probability theory in fuzzy sample space. Metrika 60 (2):167–89.MathSciNetCrossRefGoogle Scholar
  8. Näther, W. 2000. On random fuzzy variables of second order and their application to linear statistical inference with fuzzy data. Metrika 51:201–21.MathSciNetCrossRefGoogle Scholar
  9. Puri, M. D., and D. Ralescu. 1986. Fuzzy random variables. Journal of Mathematical Analysis and Applications 114:409–22.MathSciNetCrossRefGoogle Scholar
  10. Stefanini, L. 2010. A generalization of Hukuhara difference and division for interval and fuzzy arithmetic. Fuzzy Sets and Systems 161:1564–84.MathSciNetCrossRefGoogle Scholar
  11. Wang, D. 2008. An autoregressive model with fuzzy random variables. In Soft methods for handling variability and imprecision, Advances in soft computing, ed. D. Dubois et al., 48401–408. Heidelberg, Germany: Springer-Verlag.Google Scholar
  12. Wang, D., and M. Shi. 2015. Estimation of a simple multivariate linear model for fuzzy random sets. In Strengthening links between data analysis and soft computing, Advances in intelligent systems and computing, ed. P. Grzegorzewski et al., Vol. 315, 201–8. New York, NY: Springer.Google Scholar
  13. Wang, D., and M. Yasuda. 2004. Some asymptotic properties of point estimation with n-dimensional fuzzy data. Statistics 38 (2):167–81.MathSciNetCrossRefGoogle Scholar

Copyright information

© Grace Scientific Publishing, 20 Middlefield Ct, Greensboro, NC 27455 2018

Authors and Affiliations

  1. 1.School of Economics and Statistics and Lingnan Research Center for Statistical ScienceGuangzhou UniversityGuangzhouPR China

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