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Fuzzy time series forecasting is one of the most applied extensions of the fuzzy set theory. Since it is first introduced by Song and Chissom [1,2], several improvements are indicated by many scholars and its practical popularity increases gradually. While the FTS methods are applied for many different problems, fundamental drawbacks are found in t...
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... 4. Calculate the forecasted values under the three defuzzification rules. Figure 1 illustrates the working process of a univariate FTS model. The actual dataset is converted to the fuzzy clusters such as "A", "B" and "C", and then the first order ...
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... chart. The FLR groups (FLRGs) consist of FLRs with the identical LHS. In the given example, the FLRG of leading set "A" have two cases in the historical data (sample period). If the leading set "A" is found in the post-sample period, then the prediction is average of the previous outcomes of the lead-lag relationship (See right below corner of Fig. ...
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... Once the model's parameters are learned, the model is applied to extrapolate the time series' future values. During the past several decades, researchers have dedicated much effort to boost forecasting accuracy and proposed numerous novel models, such as ARIMA [1], support vector machine [2,3], fuzzy time series [4,5], fuzzy cognitive maps [6,7], neural networks [8][9][10][11][12][13][14][15][16][17], and hybrid models [18][19][20]. Among these models, neural networks have shown tremendous success in time series forecasting. ...
The challenge of accurately forecasting a time series covers numerous disciplines, from economics to engineering. Among the thousands of machine learning models, random vector functional link (RVFL) is a robust and efficient model which has demonstrated its success in various challenging forecasting problems. RVFL is an efficient universal function appropriator that randomly generates the weights between the input and hidden layers. However, RVFL still lacks the strong ability to extract meaningful multi-scale features from input data because of the single-layer random mapping of enhancement nodes. Therefore, we propose to combine the empirical wavelet transformation (EWT) with RVFL to strengthen the multi-scale feature extraction ability. The EWT can decompose the original time series into several sub-series which carry the information of different frequencies. Besides, we propose a walk-forward decomposition mechanism to implement the EWT. By introducing such a walk-forward mechanism and the combination of EWT and RVFL, the hybrid model achieves high accuracy and averts the data leakage problem during forecasting. A detailed and comprehensive empirical study on twenty-six public time series validates the proposed model’s superiority compared with ten popular baseline models from the literature.
... The selection of the hyperparameter k impact directly on the model accuracy and parsimony, as discussed in Duru and Yoshida [2012]. The number of partitions impact on the model parsimony directly and, for instance, given a rule model the maximum number of rules is the cartesian product between the fuzzy sets A j ∈Ã for each order Ω. ...
... This is relevant because all methods presented before are time invariant models, which assume that Y is stationary. Indeed, this is, according to Duru and Yoshida [2012], one of the greatest weakness of the FTS methods. The differentiation can be used to make Y stationary and can be employed as pre and post processing of almost all FTS methods, being in some cases explicitly part of the model, as in Cheng et al. [2011], Lee and Javedani [2011], Sadaei et al. [2016b]. ...
In the field of time series forecasting, the most known methods are based on pointforecasting. However, this kind of forecasting has a serious drawback: it does not quantifythe uncertainties inherent to natural and social processes neither other uncertaintiescaused by the data gathering and processing. Because this in last years the interval andprobabilistic forecasting methods have been gaining more attention of researches, speciallyon environmental and economical sciences. But these techniques also have their own issuesdue to the methods being black-boxes and requiring stochastic simulations and ensemblesof multiple forecasting methods which are computationally expensive.On the other hand, the data volume (number of instances) and dimensionality (numberof variables) have reached magnitudes even greater, due to the commoditizing of thecapturing and storing computational devices, in a phenomenon known as Big Data. Suchfactors impact directly on the model’s training and updating costs, and for time serieswith Big Data characteristics, the scalability became a decisive factor in the choosing ofpredictive methods.In this context the Fuzzy Time Series (FTS) methods emerge, which have been growing inrecent years due to their accurate results, easiness of implementation, low computationalcost and model explainability. The Fuzzy Time Series methods have been applied toforecast electric load, market assets, economical indicators, tourism demand etc. But thereis a lack on FTS literature regarding interval and probabilistic forecasting.This thesis proposes new scalable Fuzzy Time Series methods and discusses its applicationto point, interval and probabilistic forecasting of mono and multivariate time series, for oneto many steps ahead. The parameters and hyper-parameters are discussed and fine tunningalternatives are presented. Finally the proposed methods are compared with the mainFuzzy Time Series techniques and other literature approaches using environmental andstock market data. The proposed methods obtained promising results on point, intervaland probabilistic forecasting and presented low computational cost, making it useful for awide range of applications.
... In most of the above studies, historical data were used directly to train ANFIS model; thus, the non-stationarity of the data was ignored. Stefanakos and Schinas (2015) and Duru and Yoshida (2012) conducted a series of studies and proved that non-stationarity is inherent in time series of wind and wave parameters due to the seasonal effect. Therefore, prior to forecasting, the non-stationarity should be removed from the initial time series. ...
Short-term predictions of wind and wave properties with a duration of 1–3 days are vital for decision-making during the execution of marine operations. One-step-ahead weather conditions can be accurately predicted via various methods. However, prediction over long horizons is challenging since multi-step-ahead prediction is typically faced with growing uncertainties. In this study, a hybrid method for predicting multi-step-ahead wind and wave conditions is proposed, which combines a decomposition technique and the adaptive-network-based fuzzy inference system (ANFIS). First, the decomposition technique is applied to obtain stationary time series. Then, multi-step-ahead forecasting is conducted using ANFIS, in which three multi-step-ahead models (the M-1, M-N and M-1 slope models) are employed. To quantify the forecast uncertainty, the mean value and standard deviation of the error factor are calculated. The proposed method is evaluated by multi-step-ahead predictions within 24 h of wind and wave conditions at the North Sea center utilizing hourly time series of the mean wind speed Uw, the significant wave height Hs and the spectral peak period Tp. The results demonstrate that the forecast uncertainty increases with the prediction horizon, and a prediction range determined by the error factor provides a basic reference for the use of predicted environmental conditions for marine operations.
... Usually in Fuzzy Time Series (FTS) studies, the nonstationarity is neglected. In contrast, the authors in [35][36][37] consider that nonstationarity should be removed from the initial time series, before starting the fuzzy forecasting procedure; especially in time series of wind and wave parameters where the nonstationary character is inherent due to the seasonal effect. So, in these works, fuzzy techniques were combined with an existing nonstationary modelling of wind and wave parameters to improve the forecasting procedure. ...
Global climate change may have serious impact on human activities in coastal and other areas. Climate change may affect the degree of storminess and, hence, change the wind-driven ocean wave climate. This may affect the risks associated with maritime activities such as shipping and offshore oil and gas. So, there is a recognized need to understand better how climate change will affect such processes. Typically, such understanding comes from future projections of the wind and wave climate from numerical climate models and from the stochastic modelling of such projections. This work investigates the applicability of a recently proposed nonstationary fuzzy modelling to wind and wave climatic simulations. According to this, fuzzy inference models (FIS) are coupled with nonstationary time series modelling, providing us with less biased climatic estimates. Two long-term datasets for an area in the North Atlantic Ocean are used in the present study, namely NORA10 (57 years) and ExWaCli (30 years in the present and 30 years in the future). Two distinct experiments have been performed to simulate future values of the time series in a climatic scale. The assessment of the simulations by means of the actual values kept for comparison purposes gives very good results.
... Many researchers do not consider its importance, and the stationarity is sometimes stated as an unnecessary condition for the FTS. In contrast, Duru and Yoshida (2012), and the authors of this paper, consider that nonstationarity should be first removed from the initial time series, before starting the fuzzy forecasting procedure. ...
This work explores the applicability of well-known fuzzy time series forecasting techniques for the prediction of bunker prices. These techniques have extensively been used with great success to the forecasting of stock prices. In the present work, weekly time series of bunker prices in four major world ports (Rotterdam, Houston, Singapore, and Fujairah) have been thoroughly examined and used for the verification of the forecasting performance of the fuzzy models. The following bunker types have been examined: 380cSt (high and low sulphur), 180cSt (high sulphur), marine diesel oil (MDO), and marine gas oil (MGO). To examine the forecasting accuracy, four error measures are used as an evaluation criterion to compare the forecasting performance of the listing models. Before applying the fuzzy forecasting procedure, and in order to remove nonstationarity, both differencing and moving-average are applied to the data. It has been found that all four error measures attain their minimum at the same point M
opt, which in turn gives the closer forecasts to the actual values. As the importance of fuel prices increases, effective forecasting could further benefit operators with compliance issues and financial planning as well as regulators estimating better the timing and the cost of regulation.
... Rather than a pure engineering approach, this paper follows an integrative perspective between the theoretical forecasting, business practice and the superiority of engineering as an instrument. Based on the principles of forecasting [32], post-sample control, stationarity control, benchmark selection and accuracy metric selection are performed accordingly. The practical users cannot easily deal with complexities, initial numbers/inputs and other kind of user settings. ...
... Many researchers do not consider its importance, and the stationarity is sometimes stated as an unnecessary condition for the FTS. In contrast, Duru and Yoshida (2012), and the authors of this paper, consider that nonstationarity should be first removed from the initial time series, before starting the fuzzy forecasting procedure. ...
This work explores the applicability of well-known fuzzy time series forecasting techniques for the prediction of bunker prices. These techniques have extensively been used with great success to the forecasting of stock prices. In the present work, the prices of bunkers of high-sulfur and low-sulfur, 380cSt grades and at the bunkering spots of Rotterdam and Houston are thoroughly examined and used for the verification of the forecasting performance of the fuzzy models. To examine the forecasting accuracy, the root mean squared error (RMSE) and the mean absolute percentage error (MAPE) are used as an evaluation criterion to compare the forecasting performance of the listing models. As the importance of fuel prices increases, effective forecasting could further benefit operators with compliance issues and financial planning as well as regulators estimating better the timing and the cost of regulation.
