In recent years, many studies have been done on forecasting fuzzy time series. First order fuzzy time series forecasting methods with first-order lagged variables and high order fuzzy time series forecasting methods with consecutive lagged variables constitute the considerable part of these studies. However, these methods are not effective in forecasting fuzzy time series which contain seasonal structures. In this respect, it would be more appropriate to use methods that consider the seasonal relations in seasonal fuzzy time series forecasting. Although seasonal fuzzy time series forecasting methods exist in literature, these methods use equal interval lengths in partition of the universe of discourse. This situation incapacitates the performance of the method in forecasting time series including seasonality and trend. In this study, a new fuzzy time series forecasting method in which intervals constituting partition of the universe of discourse increase in time at a rate that obtained based on optimization was proposed. The proposed method was applied to two real time series and obtained results were compared with other methods and the superior performance of the proposed method was proved.

Improving time series forecasting accuracy is an important yet often dicult task. Both theoretical and empirical ndings have indicated that integration of several models is an e ective way to improve predictive performance, especially when the models in combination are quite di erent. In this paper, a model of the hybrid arti cial neural networks and fuzzy model is proposed for time series forecasting, using autoregressive integrated moving average models. In the proposed model, by rst modeling the linear components, autoregressive integrated moving average models are combined with the these hybrid models to yield a more general and accurate forecasting model than the traditional hybrid arti cial neural networks and fuzzy models. Empirical results for nancial time series forecasting indicate that the proposed model exhibits e ectively improved forecasting accuracy and hence is an appropriate forecasting tool for nancial time series forecasting.

Time series forecasting is an active research area that has drawn considerable attention for applications in a variety of areas. Forecasting accuracy is one of the most important features of forecasting models. Nowadays, despite the numerous time series forecasting models which have been proposed in several past decades, it is widely recognized that financial markets are extremely difficult to forecast. Artificial Neural Networks (ANNs) are flexible computing frameworks and universal approximators that can be applied to a wide range of forecasting problems with a high degree of accuracy. However, using ANNs to model linear problems have yielded mixed results, and hence; it is not wise to apply them blindly to any type of data. Improving forecasting especially time series forecasting accuracy is an important yet often difficult task facing decision makers in many areas. Both theoretical and empirical findings have suggested that integration of different models can be an effective method of improving upon their predictive performance, especially when the models in the ensemble are quite different. This is the reason that hybrid methodologies combining the linear models such as ARIMA and nonlinear models such as ANNs have been proposed in the literature of time series forecasting. These hybrid techniques decompose a time series into its linear and nonlinear form in order to use the unique advantages of linear and nonlinear modeling methods and are one of the most popular hybrid models, which have recently been shown to be successful for single models. In this paper, an improved version of the hybrid ANNs/ARIMA models is proposed for time series forecasting. In the proposed model, the performance of the hybrid ANNs/ARIMA models is improved using diagnosing the trend of residuals by Probabilistic Neural Networks (PNNs). Empirical results of exchange rate forecasting indicate that the proposed model is more satisfactory than ANNs/ARIMA models.

Rivers flow forecasting has special importance in surface water management، especially in agricultural planning and risk reduction of floods and droughts. In recent years، studies have shown the superiority of time-series forecasting models based on artificial intelligence، such as artificial neural networks (ANN) and genetic programming (GP). In this paper، continuous and discrete historical flow records are used for Saeed-Abad monthly river flow forecasting in East Azarbaijan province، Iran. Auto regressive moving average with exogenous inputs (ARMAX)، ANN، and GP models are used and compared to each other. Coefficient of determination (R2) and root mean square error (RMSE) are used to evaluate the performance of the aforementioned models. Results show that for the two methods، the GP model is more effective than ARMAX and ANN in terms of accuracy. For continuous time-series forecasting، GP is a more precise model (R2 = 0. 7 and RMSE = 0. 172) than either ANN (R2 = 0. 627 and RMSE = 0. 193) or ARMAX (R2 = 0. 595 and RMSE = 0. 243). For discrete time-series forecasting، the superiority of the GP model is evident in almost all months. Moreover، results indicate that discrete monthly time-series forecasting method is superior to the continuous monthly time-series forecasting method.

Demand forecasting is a vital task for firms to manage the optimum quantity of raw material and products. The demand forecasting task can be formulated as a time series forecasting problem by measuring historical demand data at equal intervals. Demand time series usually exhibit a seasonal pattern. The principle idea of this study is to propose a method that predicts the demand for every different season using a specialized forecaster. In this study, we test our proposal using the Long Short-Term Memory (LSTM) which is a deep learning technique for time series forecasting. Specifically, the proposed method instead of learning an LSTM model using the whole demand data builds a specialized LSTM model corresponding to each season. The proposed method is evaluated using different topologies of the LSTM model. The results of experiments indicated that the proposed method outperforms the regular method considering the performance measures. The proposed method can be used in other domains for demand forecasting.

Both theoretical and empirical findings have suggested that combining different models can be an effective way to improve the predictive performance of each individual model. It is especially occurred when the models in the ensemble are quite different. Hybrid techniques that decompose a time series into its linear and nonlinear components are one of the most important kinds of the hybrid models for time series forecasting. Several researches in the literature have been shown that these models can outperform single models. In this paper, the predictive capabilities of three different models in which the autoregressive integrated moving average (ARIMA) as linear model is combined to the multilayer perceptron (MLP) as nonlinear model, are compared together for time series forecasting. These models are including the Zhang’s hybrid ANNs/ARIMA, artificial neural network (p,d,q), and generalized hybrid ANNs/ARIMA models. The empirical results with three well-known real data sets indicate that all of these methodologies can be effective ways to improve forecasting accuracy achieved by either of components used separately. However, the generalized hybrid ANNs/ARIMA model is more accurate and performs significantly better than other aforementioned models.

With the increasing importance of forecasting with the utmost degree of accuracy, utilizing hybrid frameworks become a must for obtaining more accurate and more reliable forecasting results. Series hybrid methodology is one of the most widely-used hybrid approaches that has encountered a great amount of popularity in the literature of time series forecasting and has been applied successfully in a wide variety of domains. In such hybrid methods is assumed that there is an additive relationship among different components of time series. Thus, based on this assumption, various individual models can apply separately on decomposed components, and the final forecast can be obtained. However, developed series hybrid models in the literature are constructed based on the decomposing time series into linear and nonlinear parts and generating linear-nonlinear modeling order for decomposed parts. Another assumption considered in the traditional series model is assigning equal weights to each model used for modeling linear and nonlinear components. Thus, contrary to traditional series hybrid models, to improve the performance of series hybrid models, these two basic assumptions have been violated in this paper. This study aims to propose a novel weighted MLP-ARIMA model filling the gap of series hybrid models by changing the order of sequence modeling and assigning weight for each component. Firstly, the modeling order is changed to nonlinear-linear, and then Multi-Layer Perceptron Neural Network (MLPNN) -Auto-Regressive Integrated Moving Average(ARIMA) models are employed to model and process nonlinear and linear components respectively. Secondly, each model's weights are computed by the Ordinary Least Square (OLS) weighting algorithm. Thus, in this paper, a novel improved weighted MLP-ARIMA series hybrid model is proposed for time series forecasting. The real-world benchmark data sets, including Wolf's sunspot data, the Canadian lynx data, and the British pound/US dollar exchange rate data, are elected to verify the effectiveness of the proposed weighted MLP-ARIMA series hybrid model. The simulation results revealed that the weighted MLP-ARIMA model could obtain superior performance compared to ARIMA-MLP, MLP-ARIMA, as well as the ARIMA and MLPNN individual models. The proposed hybrid model can be an effective alternative to improve forecasting accuracy obtained by traditional series hybrid methods.

Parametric models are considered the widespread methods for time series forecasting. Non-parametric or machine learning methods have significantly replaced statistical methods in recent years. In this study, we develop a novel two-level clustering algorithm to forecast short-length time series datasets using a multi-step approach, including clustering, sliding window, and MLP neural network. In first-level clustering, the time series dataset in the training part is clustered. Then, we made a long time series by concatenating the existing time series in each cluster in the first level. After that, using a sliding window, every long-time series created in the previous step is restructured to equal-size sub-series and clustered in the second level. Applying an MLP network, a model has been fitted to final clusters. Finally, the test data distance is calculated with the center of the final cluster, selecting the nearest distance, and using the fitted model in that cluster, the final forecasting is done. Using the WAPE index, we compare the one-level clustering algorithm in the literature regarding the mean of answers and the best answer in a ten-time run. The results reveal that the algorithm could increase the WAPE index value in terms of the mean and the best solution by 8.78% and 5.24%, respectively. Also, comparing the standard deviation of different runs shows that the proposed algorithm could be further stabilized with a 3.24 decline in this index. This novel study proposed a two-level clustering for forecasting short-length time series datasets, improving the accuracy and stability of time series forecasting.

In a business environment where there is fierce competition between companies, accurate demand forecasting is vital. If we collect customer demand data at discrete points in time, we obtain a demand time series. As a result, the demand forecasting problem can be formulated as a time series forecasting task. In the context of time series forecasting, deep learning methods have demonstrated good accuracy in predicting complex time series. However, the excellent performance of these methods is dependent on the amount of data available. For this purpose, in this study, we propose to use time series augmentation techniques to improve the performance of deep learning methods. In this study, three new methods have been used to test the effectiveness of the proposed approach, which are: 1) Long short-term memory, 2) Convolutional network 3) Multihead self-attention mechanism. This study also uses a multi-step forecasting approach that makes it possible to predict several future points in a forecasting operation. The proposed method is applied to the actual demand data of a furniture company. The experimental results show that the proposed approach improves the forecasting accuracy of the methods used in most different prediction scenarios

The evolution of financial data shows a high degree of volatility of the series, coupled with increasing difficulties of forecasting financial variables. Some alternative forecasting methods, based on the literature review, have been developed, which can be particularly useful in the analysis of financial time series. Despite of the numerous time series forecasting models, the accuracy of time series forecasting is fundamental to many decision processes. Selecting an efficient technique in unique situations is very difficult task for forecasters. Many researchers have integrated linear and nonlinear methods in order to yield more accurate results. In practice, it is difficult to determine the time series under study are generated from a linear or nonlinear underlying process while many aspects of economic behavior may not be pure linear or nonlinear. Although both ARIMA and Artificial Neural Networks (ANNs) models have the flexibility in modeling a variety of problems, none of which is universally the best model used indiscriminately in every forecasting situation. In this paper, based on the foundations of ARIMA and ANNs models, a hybrid method is proposed to forecast exchange rate. Empirical results indicate that integrating linear and nonlinear ARIMA and Artificial Neural Networks (ANNs) models can be an effective way to improve forecasting accuracy achieved by either of the above linear and nonlinear models used separately.