A note on autoregressive models with fuzzy random variables

Wang, Dabuxilatu

doi:10.1080/15598608.2017.1389664

Cited by 1 publication

(4 citation statements)

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“…To verify the effectiveness of the proposed linguistic-valued ARMA models, we applied them to forecast the linguistic monthly Hang Seng Index (HSI) with an empirical analysis, and detailed comparisons of the models with other classical AR(1), AR(2), AR(3) models, as well as the ARMA(1,1) model, are given. Furthermore, we present theoretical proofs for some conclusions on the convergence properties of the sequence of the FRVs mentioned in this paper [10].…”

Section: Discussionmentioning

confidence: 97%

“…The study of the fuzzy set-valued time series modeling is just in its infancy. There are only two estimated fuzzy set-valued models like AR(1) and ARMA(1,1) [10,11] that can be considered for model comparison under special conditions. However, it is obvious here that the fuzzy set-valued ARMA(1,1) model is better than the fuzzy set-valued AR(1) model for the forecast of the linguistic monthly HSI data.…”

Section: Stepmentioning

confidence: 99%

“…However, there was no work on the model's estimation. Wang [10] further noted that former autoregressive models contain some deficiencies, so the model was complemented with an ARMA model and its primary application in financial market forecasting was proposed. Jung et al [11] also considered a unified approach to asymptotic behavior for parameter estimation for an AR(1) model of a fuzzy number-valued time series, where a brief outline on the modeling of time series with fuzzy number inputs and fuzzy number outputs was given.…”

Section: Introductionmentioning

confidence: 99%

“…We are aware that there are several fundamental problems, such as parameter estimation (model estimation), asymptotic properties of the estimators, etc., which remain to be investigated further. For instance, parameter estimation has been carried out only for the AR(1) and ARMA(1,1) models with fuzzy data [10,11], and the asymptotic properties (consistency properties) of the estimators have been obtained only for the AR(1) model with fuzzy data [11]. In this study, based on previous works [7,10,11], we firstly investigated the asymptotic properties of the estimators for a (1,1)-order autoregressive moving average model ARMA(1,1) based on linguistic data (fuzzy data), then used the justified ARMA(1,1) model to forecast the future of the HSI with a simulation analysis.…”

Section: Introductionmentioning

confidence: 99%

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

Wang

Liang

2018

Symmetry

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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.

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Section: Discussionmentioning

confidence: 97%

Section: Stepmentioning

confidence: 99%