Next Article in Journal
Lower Bounds for Gaussian Estrada Index of Graphs
Previous Article in Journal
Temperature-Dependent s±s++ Transitions in the Multiband Model for Fe-Based Superconductors with Impurities
Article Menu

Export Article

Open AccessArticle
Symmetry 2018, 10(8), 324; https://doi.org/10.3390/sym10080324

A Fuzzy Set-Valued Autoregressive Moving Average Model and Its Applications

1
Department of Statistics, Guangzhou University, No. 230 Waihuanxi Road, Higher Education Mega Center, Guangzhou 510006, China
2
School of Applied Mathematics, Guangdong University of Technology, No. 161 Yinglong Road, Tianhe District, Guangzhou 510520, China
*
Author to whom correspondence should be addressed.
Received: 23 June 2018 / Revised: 19 July 2018 / Accepted: 2 August 2018 / Published: 7 August 2018
View Full-Text   |   Download PDF [347 KB, uploaded 7 August 2018]   |  

Abstract

Autoregressive moving average (ARMA) models are important in many fields and applications, although they are most widely applied in time series analysis. Expanding the ARMA models to the case of various complex data is arguably one of the more challenging problems in time series analysis and mathematical statistics. In this study, we extended the ARMA model to the case of linguistic data that can be modeled by some symmetric fuzzy sets, and where the relations between the linguistic data of the time series can be considered as the ordinary stochastic correlation rather than fuzzy logical relations. Therefore, the concepts of set-valued or interval-valued random variables can be employed, and the notions of Aumann expectation, Fréchet variance, and covariance, as well as standardized process, were used to construct the ARMA model. We firstly determined that the estimators from the least square estimation of the ARMA (1,1) model under some L2 distance between two sets are weakly consistent. Moreover, the justified linguistic data-valued ARMA model was applied to forecast the linguistic monthly Hang Seng Index (HSI) as an empirical analysis. The obtained results from the empirical analysis indicate that the accuracy of the prediction produced from the proposed model is better than that produced from the classical one-order, two-order, three-order autoregressive (AR(1), AR(2), AR(3)) models, as well as the (1,1)-order autoregressive moving average (ARMA(1,1)) model. View Full-Text
Keywords: stochastic process; fuzzy sets; autoregressive model; forecasting stochastic process; fuzzy sets; autoregressive model; forecasting
Figures

Figure 1

This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).
SciFeed

Share & Cite This Article

MDPI and ACS Style

Wang, D.; Zhang, L. A Fuzzy Set-Valued Autoregressive Moving Average Model and Its Applications. Symmetry 2018, 10, 324.

Show more citation formats Show less citations formats

Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Related Articles

Article Metrics

Article Access Statistics

1

Comments

[Return to top]
Symmetry EISSN 2073-8994 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top