Modeling autoregressive fuzzy time series data based on semi-parametric methods

Zarei, Reza; Akbari, Masoumeh; Chachi, Jalal

doi:10.1007/s00500-019-04349-w

Cited by 11 publications

(11 citation statements)

References 27 publications

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“…Remark 2. Since the proposed time series model relies on fuzzy data, let us recall the previous time series models based on fuzzy data [66][67][68]. First, Hesamian and Akbari [66] proposed a fuzzy semi-parametric autoregressive integrated moving average (ARIMA) model as follows:…”

Section: The Modelmentioning

confidence: 99%

“…In this regard, Hesamian and Akbari [66] first suggested a fuzzy semi-parametric time series model (FSPTSM) based on fuzzy data, non-fuzzy coefficients, and fuzzy smooth functions. Secondly, Zarei et al [67] used a specific variant of the FSPTSM [66] for triangular fuzzy data and different distance measures for fuzzy data. And thirdly, Hesamian et al [68] introduced a forward additive time series model (FATSM) for fuzzy observations.…”

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confidence: 99%

“…The advantage of this methodology is that it considerably decreases the complexity in the estimation procedure. While the other fuzzy time series models [66][67][68] are based on estimating the unknown components of the model by unifying the centers and spreads of fuzzy data and their corresponding predicted values, our proposed method provides a smooth estimation procedure according to three separate stages. In the framework of a simulation study and two real-data examples, the efficiency and appropriateness of the FNPTSM is assessed in comparison with previous time series models for fuzzy data by utilizing four approved goodness-of-fit criteria.…”

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confidence: 99%

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A Three-Stage Nonparametric Kernel-Based Time Series Model Based on Fuzzy Data

2023

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In this paper, a nonlinear time series model is developed for the case when the underlying time series data are reported by LR fuzzy numbers. To this end, we present a three-stage nonparametric kernel-based estimation procedure for the center as well as the left and right spreads of the unknown nonlinear fuzzy smooth function. In each stage, the nonparametric Nadaraya–Watson estimator is used to evaluate the center and the spreads of the fuzzy smooth function. A hybrid algorithm is proposed to estimate the unknown optimal bandwidths and autoregressive order simultaneously. Various goodness-of-fit measures are utilized for performance assessment of the fuzzy nonlinear kernel-based time series model and for comparative analysis. The practical applicability and superiority of the novel approach in comparison with further fuzzy time series models are demonstrated via a simulation study and some real-life applications.

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Section: The Modelmentioning

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A Three-Stage Nonparametric Kernel-Based Time Series Model Based on Fuzzy Data

2023

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“…( 3) is solved for the datset of 6), ( 7), and ( 8) are minimized for such a dataset, respectively. Now, the following well-known criteria for evaluation of goodness-of-fit of fuzzy regression models are employed to compare the performance values of the competitive models (Akbari and Hesamian 2018;Chachi andTaheri 2013, 2021;Taheri and Chachi 2021;Zarei et al 2020) The goodness-of-fit values of the estimated models are tabulated in Table 3. Here, we will explain a summarized computation to show how the values of G 1 , G 2 and G 3 are obtained, for instance, for the model proposed by Arefi (2020).…”

Section: Alternativesmentioning

confidence: 99%

“…Model performance analysis is of crucial importance when dealing with different model estimation procedures which have been highly affected by the input-output values of dataset. Till now, a single experimental goodness-of-fit formula is used to compare the observed values with the model predictions to examine and compare the accuracy and performance of fuzzy regression models (Arefi 2020;Chachi 2019;Chachi and Taheri 2021;Taheri and Chachi 2021; D'Urso and Leski 2020; Akbari and Hesamian 2018;Khammar et al 2020;Jiang et al 2019;Zarei et al 2020). The results of the goodness-of-fit formula were further used to lead to a decision on selecting the best model in comparative studies.…”

Section: Introductionmentioning

confidence: 99%

MADM approach to analyse the performance of fuzzy regression models

Kazemifard

Chachi

2021

J Ambient Intell Human Comput

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It is worth to note that estimated parameters of any fuzzy regression model as well as its goodness-of-fit value depend on the objective function being optimized. Thus, it is not easy to compare the solutions of different models that optimize different objective functions. On the other hand, dataset has a significant influence on the performance of any model estimation procedure making the comparison more challengeable. In this paper, we propose a method in order to compare and/or rank a set of fuzzy regression models based on their goodness-of-fit performance analysis when applied to modeling a dataset. With regard to that, the problem of finding the most preferred/desirable model is considered as a multi-attribute decision making (MADM) problem in which the set of candidate models are alternatives and the goodness-of-fit criteria are attributes. Attribute values are calculated based on well-known goodness-of-fit formula while their weights, which are considered as the most important points in MADM problems, are calculated by the entropy measure. Therefore, the entries of the decision matrix are considered as the fitness values of the data points by the models (or alternatives). The entropy values are then transformed to the weight values of the data points illustrating the importance of each data point in the estimation methods of models. Ultimately, the TOPSIS method is employed to provide an algorithm to rank the models. The proposed method not only gives us the rank of the models, but also provides us an index showing how much each ranked model fits the data set.

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