Combining seasonal ARIMA models with computational intelligence techniques for time series forecasting

Seasonal autoregressive integrated moving average (SARIMA) models form one of the most popular and widely used seasonal time series models over the past three decades. However, in several researches it has been argued that they have two basic limitations that detract from their popularity for seasonal time series forecasting tasks. SARIMA models assume that future values of a time series have a linear relationship with current and past values as well as with white noise; therefore, approximations by SARIMA models may not be adequate for complex nonlinear problems. In addition, SARIMA models require a large amount of historical data to produce desired results. However, in real situations, due to uncertainty resulting from the integral environment and rapid development of new technology, future situations must be forecasted using small data sets over a short span of time. Using hybrid models or combining several models has become a common practice to overcome the limitations of single models and improve forecasting accuracy. In this paper, a new hybrid model, which combines the seasonal autoregressive integrated moving average (SARIMA) and computational intelligence techniques such as artificial neural networks and fuzzy models for seasonal time series forecasting is proposed. In the proposed model, these two techniques are applied to simultaneously overcome the linear and data limitations of SARIMA models and yield more accurate results. Empirical results of forecasting two well-known seasonal time series data sets indicate that the proposed model exhibits effectively improved forecasting accuracy, so that it can be used as an appropriate seasonal time series model.     

An artificial neural network (p, d, q) model for timeseries forecasting

Artificial neural networks (ANNs) are flexible computing frameworks and universal approximators that can be applied to a wide range of time series forecasting problems with a high degree of accuracy. However, despite all advantages cited for artificial neural networks, their performance for some real time series is not satisfactory. Improving forecasting especially time series forecasting accuracy is an important yet often difficult task facing forecasters. Both theoretical and empirical findings have indicated that integration of different models can be an effective way of improving upon their predictive performance, especially when the models in the ensemble are quite different. In this paper, a novel hybrid model of artificial neural networks is proposed using auto-regressive integrated moving average (ARIMA) models in order to yield a more accurate forecasting model than artificial neural networks. The empirical results with three well-known real data sets indicate that the proposed model can be an effective way to improve forecasting accuracy achieved by artificial neural networks. Therefore, it can be used as an appropriate alternative model for forecasting task, especially when higher forecasting accuracy is needed.     

Predictive modeling for wastewater applications: Linear and nonlinear approaches

This study compares the multi-period predictive ability of linear ARIMA models to nonlinear time delay neural network models in water quality applications. Comparisons are made for a variety of artificially generated nonlinear ARIMA data sets that simulate the characteristics of wastewater process variables and watershed variables, as well as two real-world wastewater data sets. While the time delay neural network model was more accurate for the two real-world wastewater data sets, the neural networks were not always more accurate than linear ARIMA for the artificial nonlinear data sets. In some cases of the artificial nonlinear data, where multi-period predictions are made, the linear ARIMA model provides a more accurate result than the time delay neural network. This study suggests that researchers and practitioners should carefully consider the nature and intended use of water quality data if choosing between neural networks and other statistical methods for wastewater process control or watershed environmental quality management.     

A hybrid SARIMA wavelet transform method for sales forecasting

Time series forecasting, as an important tool in many decision support systems, has been extensively studied and applied for sales forecasting over the past few decades. There are many well-established and widely-adopted forecasting methods such as linear extrapolation and SARIMA. However, their performance is far from perfect and it is especially true when the sales pattern is highly volatile. In this paper, we propose a hybrid forecasting scheme which combines the classic SARIMA method and wavelet transform (SW). We compare the performance of SW with (i) pure SARIMA, (ii) a forecasting scheme based on linear extrapolation with seasonal adjustment (CSD + LESA), and (iii) evolutionary neural networks (ENN). We illustrate the significance of SW and establish the conditions that SW outperforms pure SARIMA and CSD + LESA. We further study the time series features which influence the forecasting accuracy, and we propose a method for conducting sales forecasting based on the features of the given sales time series. Experiments are conducted by using real sales data, hypothetical data, and publicly available data sets. We believe that the proposed hybrid method is highly applicable for forecasting sales in the industry.     

Pattern similarity-based methods for short-term load forecasting – Part 2: Models

Models for the short-term load forecasting based on the similarity of patterns of seasonal cycles are presented. They include: kernel estimation-based model, nearest neighbor estimation-based models and pattern clustering-based models such as classical clustering methods and new artificial immune systems. The problem of construction of the pattern similarity-based forecasting models and the elements and procedures of the model space are characterized. Details of the model learning and optimization using deterministic and stochastic methods such as evolutionary algorithms and tournament searching are described. Sensitivities of the models to changes in parameter values and their robustness to noisy and missing data are examined. The comparative studies with other popular forecasting methods such as ARIMA, exponential smoothing and neural networks are performed. The advantages of the proposed models are their simplicity and a small number of parameters to be estimated, which implies simple optimization procedures. The models can successfully deal with missing data. The increased number of the model outputs does not complicate their structure. The local nature of the models leads to their simplification and accuracy improvement. The proposed models are strong competitors for other popular univariate methods, which was confirmed in the simulation studies.     

Forecasting seasonal time series with computational intelligence: On recent methods and the potential of their combinations

Accurate time series forecasting is a key issue to support individual and organizational decision making. In this paper, we introduce novel methods for multi-step seasonal time series forecasting. All the presented methods stem from computational intelligence techniques: evolutionary artificial neural networks, support vector machines and genuine linguistic fuzzy rules. Performance of the suggested methods is experimentally justified on seasonal time series from distinct domains on three forecasting horizons. The most important contribution is the introduction of a new hybrid combination using linguistic fuzzy rules and the other computational intelligence methods. This hybrid combination presents competitive forecasts, when compared with the popular ARIMA method. Moreover, such hybrid model is more easy to interpret by decision-makers when modeling trended series.     

Sales forecasting system based on Gray extreme learning machine with Taguchi method in retail industry

Due to the strong competition that exists today, most retailers are in a continuous effort for increasing profits and reducing their cost. An accurate sales forecasting system is an efficient way to achieve the aforementioned goals and lead to improve the customers’ satisfaction, reduce destruction of products, increase sales revenue and make production plan efficiently. In this study, the Gray extreme learning machine (GELM) integrates Gray relation analysis and extreme learning machine with Taguchi method to support purchasing decisions. GRA can sieve out the more influential factors from raw data and transforms them as the input data in a novel neural network such as ELM. The proposed system evaluated the real sales data in the retail industry. The experimental results demonstrate that our proposed system outperform several sales forecasting methods which are based on back-propagation neural networks such as BPN and MFLN models.     

基于人工神经网络实现的QoS路由决策

讨论了基于神经网络自学习算法实现QoS路由决策的问题。为了证明利用人工神经网络优化路由决策的可行性,在由17台服务器（节点）搭建的实验网络环境中,每个节点上均设计了由几个神经元组成的神经网络,各神经元依据网络的测量数据,通过学习算法动态地进行路由决策。实验结果表明,在以最小跳转数或最小延时为QoS目标时,神经网络所提供的路由决策均可以有效地使QoS接近最优值;同时,当神经网络综合考虑延时和最小跳转数两项QoS指标时,网络延时状况要优于只考虑一项指标的情况。实验结果证明了利用神经网络在节点上进行分布式的路由     

Fuzzy GMDH-type neural network model and its application to forecasting of mobile communication

In this paper, the fuzzy group method data handling-type (GMDH) neural networks and their application to the forecasting of mobile communication systems are described. At present, the GMDH family of modeling algorithms discovers the structure of empirical models and it gives only the way to get the most accurate identification and demand forecasts in case of noised and short input sampling. In distinction to neural networks, the results are explicit mathematical models, obtained in a relative short time. In this paper, an adaptive learning network is proposed as a kind of neural-fuzzy GMDH. The proposed method can be reinterpreted as a multi-stage fuzzy decision rule which is called the neural-fuzzy GMDH. The GMDH-type neural networks have several advantages compared with conventional multi-layered GMDH models. Therefore, many types of nonlinear systems can be automatically modeled by using the neuro-fuzzy GMDH. A computer program is developed and successful applications are shown in the field of estimating problems of mobile communication with a number of factors considered.     

Forecasting building energy consumption: Adaptive long-short term memory neural networks driven by genetic algorithm

The real-world building can be regarded as a comprehensive energy engineering system; its actual energy consumption depends on complex affecting factors, including various weather data and time signature. Accurate energy consumption forecasting and effective energy system management play an essential part in improving building energy efficiency. The multi-source weather profile and energy consumption data could enable integrating data-driven models and evolutionary algorithms to achieve higher forecasting accuracy and robustness. The proposed building energy consumption forecasting system consists of three layers: data acquisition and storage layer, data pre-processing layer and data analytics layer. The core part of the data analytics layer is a hybrid genetic algorithm (GA) and long-short term memory (LSTM) neural network model for accurate and robust energy prediction. LSTM neural network is adopted to capture the interrelationship between energy consumption data and time. GA is adopted to select the optimal architecture for LSTM neural networks to improve its forecasting accuracy and robustness. The hyper-parameters for determining LSTM architecture include the number of LSTM layers, number of neurons in each LSTM layer, dropping rate of each LSTM layer and network learning rate. Meanwhile, the effects of historical weather profile and time horizon of past information are also investigated. Two real-life educational buildings are adopted to test the performance of the proposed building energy consumption forecasting system. Experiments reveal that the proposed adaptive LSTM neural network performs better than the existing feedforward neural network and LSTM-based prediction models in accuracy and robustness. It also outperforms those LSTM networks whose hyper-parameters are determined by grid search, Bayesian optimisation and PSO. Such accurate energy consumption prediction can play an essential role in various areas, including daily building energy management, decision making of facility managers, building information model designs, net-zero energy operation, climate change mitigation and circular economy.     

A hybrid neural network and ARIMA model for water quality time series prediction

Accurate predictions of time series data have motivated the researchers to develop innovative models for water resources management. Time series data often contain both linear and nonlinear patterns. Therefore, neither ARIMA nor neural networks can be adequate in modeling and predicting time series data. The ARIMA model cannot deal with nonlinear relationships while the neural network model alone is not able to handle both linear and nonlinear patterns equally well. In the present study, a hybrid ARIMA and neural network model is proposed that is capable of exploiting the strengths of traditional time series approaches and artificial neural networks. The proposed approach consists of an ARIMA methodology and feed-forward, backpropagation network structure with an optimized conjugated training algorithm. The hybrid approach for time series prediction is tested using 108-month observations of water quality data, including water temperature, boron and dissolved oxygen, during 1996–2004 at Büyük Menderes river, Turkey. Specifically, the results from the hybrid model provide a robust modeling framework capable of capturing the nonlinear nature of the complex time series and thus producing more accurate predictions. The correlation coefficients between the hybrid model predicted values and observed data for boron, dissolved oxygen and water temperature are 0.902, 0.893, and 0.909, respectively, which are satisfactory in common model applications. Predicted water quality data from the hybrid model are compared with those from the ARIMA methodology and neural network architecture using the accuracy measures. Owing to its ability in recognizing time series patterns and nonlinear characteristics, the hybrid model provides much better accuracy over the ARIMA and neural network models for water quality predictions.     

An ensemble of neural networks for weather forecasting

This study presents the applicability of an ensemble of artificial neural networks (ANNs) and learning paradigms for weather forecasting in southern Saskatchewan, Canada. The proposed ensemble method for weather forecasting has advantages over other techniques like linear combination. Generally, the output of an ensemble is a weighted sum, which are weight-fixed, with the weights being determined from the training or validation data. In the proposed approach, weights are determined dynamically from the respective certainties of the network outputs. The more certain a network seems to be of its decision, the higher the weight. The proposed ensemble model performance is contrasted with multi-layered perceptron network (MLPN), Elman recurrent neural network (ERNN), radial basis function network (RBFN), Hopfield model (HFM) predictive models and regression techniques. The data of temperature, wind speed and relative humidity are used to train and test the different models. With each model, 24-h-ahead forecasts are made for the winter, spring, summer and fall seasons. Moreover, the performance and reliability of the seven models are then evaluated by a number of statistical measures. Among the direct approaches employed, empirical results indicate that HFM is relatively less accurate and RBFN is relatively more reliable for the weather forecasting problem. In comparison, the ensemble of neural networks produced the most accurate forecasts.     

Forecasting time series using a methodology based on autoregressive integrated moving average and genetic programming

The autoregressive integrated moving average (ARIMA), which is a conventional statistical method, is employed in many fields to construct models for forecasting time series. Although ARIMA can be adopted to obtain a highly accurate linear forecasting model, it cannot accurately forecast nonlinear time series. Artificial neural network (ANN) can be utilized to construct more accurate forecasting model than ARIMA for nonlinear time series, but explaining the meaning of the hidden layers of ANN is difficult and, moreover, it does not yield a mathematical equation. This study proposes a hybrid forecasting model for nonlinear time series by combining ARIMA with genetic programming (GP) to improve upon both the ANN and the ARIMA forecasting models. Finally, some real data sets are adopted to demonstrate the effectiveness of the proposed forecasting model.     

Hybridization of autoregressive integrated moving average (ARIMA) with probabilistic neural networks (PNNs)

Autoregressive integrated moving average (ARIMA) models are one of the most important time series models applied in financial market forecasting over the past three decades. Improving forecasting especially time series forecasting accuracy is an important yet often difficult task facing forecasters. Both theoretical and empirical findings have indicated that integration of different models can be an effective way of improving upon their predictive performance, especially when the models in the ensemble are quite different. In the literature, several hybrid techniques have been proposed by combining different time series models together, in order to yield results that are more accurate. In this paper, a new hybrid model of the autoregressive integrated moving average (ARIMA) and probabilistic neural network (PNN), is proposed in order to yield more accurate results than traditional ARIMA models. In proposed model, the estimated values of the ARIMA model are modified based on the distinguished trend of the ARIMA residuals and optimum step length, which are respectively obtained from a probabilistic neural network and a mathematical programming model. Empirical results with three well-known real data sets indicate that the proposed model can be an effective way in order to construct a more accurate hybrid model than ARIMA model. Therefore, it can be used as an appropriate alternative model for forecasting tasks, especially when higher forecasting accuracy is needed.     

基于进化神经网络的短期电网负荷预测算法

本文提出了一种基于进化神经网络的短期电网负荷预测算法。该算法使用了改进的人工蜂群算法与BP神经网络融合生成的进化神经网络,并且使用改进的人工蜂群算法对进化神经网络的偏置和权重进行优化。该算法将火电历史负荷数据作为输入,使用进化神经网络训练预测模型,预测未来一段时间内的电网负荷。首先获取历史负荷数据,然后将收集到的数据应用于进化神经网络模型训练。人工蜂群算法作为一种全局搜索算法,可以有效地探索模型参数空间,寻找最佳的模型参数组合以提升预测精度。为了验证所提出的负荷预测方法的有效性,本文使用了火电网负荷数据进行测试。实验结果表明,在短期电网负荷预测方面,本文提出的进化神经网络比传统方法预测结果更加准确可靠。     

Supervised Learning Probabilistic Neural Networks

This study proposed supervised learning probabilistic neural networks (SLPNN) which have three kinds of network parameters: variable weights representing the importance of input variables, the reciprocal of kernel radius representing the effective range of data, and data weights representing the data reliability. These three kinds of parameters can be adjusted through training. We tested three artificial functions as well as 15 benchmark problems, and compared it with multi-layered perceptron (MLP) and probabilistic neural networks (PNN). The results showed that SLPNN is slightly more accurate than MLP, and much more accurate than PNN. Besides, the data weights can find the noise data in data set, and the variable weights can measure the importance of input variables and have the greatest contribution to accuracy of model among the three kinds of network parameters.     

模糊神经网络与SARIMA结合的时间序列预测模型

模糊神经网络和SARIMA模型分别对非线性和线性时间序列有很好的预测能力,但在实际应用中大多数序列并非稳定、单纯线性或非线性的。为了提高预测精度,提出了一种基于T-S模糊神经网络与SARIMA结合的时间序列预测模型。针对悉尼航班乘客收入数据给出了三种混合模型,并与模糊神经网络、支持向量机、SARIMA和BP神经网络四种单独模型进行比较。实验结果表明,从预测精度和参数选择方面来看,所给模型是有效的。     

A hybrid extreme learning machine model with harris hawks optimisation algorithm: an optimised model for product demand forecasting applications

Accurate and real-time product demand forecasting is the need of the hour in the world of supply chain management. Predicting future product demand from historical sales data is a highly non-linear problem, subject to various external and environmental factors. In this work, we propose an optimised forecasting model - an extreme learning machine (ELM) model coupled with the Harris Hawks optimisation (HHO) algorithm to forecast product demand in an e-commerce company. ELM is preferred over traditional neural networks mainly due to its fast computational speed, which allows efficient demand forecasting in real-time. Our ELM-HHO model performed significantly better than ARIMA models that are commonly used in industries to forecast product demand. The performance of the proposed ELM-HHO model was also compared with traditional ELM, ELM auto-tuned using Bayesian Optimisation (ELM-BO), Gated Recurrent Unit (GRU) based recurrent neural network and Long Short Term Memory (LSTM) recurrent neural network models. Different performance metrics, i.e., Root Mean Squared Error (RMSE), Mean Absolute Percentage Error (MAPE) and Mean Percentage Error (MPE) were used for the comparison of the selected models. Horizon forecasting at 3 days and 7 days ahead was also performed using the proposed approach. The results revealed that the proposed approach is superior to traditional product demand forecasting models in terms of prediction accuracy and it can be applied in real-time to predict future product demand based on the previous week’s sales data. In particular, considering RMSE of forecasting, the proposed ELM-HHO model performed 62.73% better than the statistical ARIMA(7,1,0) model, 40.73% better than the neural network based GRU model, 34.05% better than the neural network based LSTM model, 27.16% better than the traditional non-optimised ELM model with 100 hidden nodes and 11.63% better than the ELM-BO model in forecasting product demand for future 3 months. The novelty of the proposed approach lies in the way the fast computational speed of ELMs has been combined with the accuracy gained by tuning hyperparameters using HHO. An increased number of hyperparameters has been optimised in our methodology compared to available models. The majority of approaches to improve the accuracy of ELM so far have only focused on tuning the weights and the biases of the hidden layer. In our hybrid model, we tune the number of hidden nodes, the number of input time lags and even the type of activation function used in the hidden layer in addition to tuning the weights and the biases. This has resulted in a significant increase in accuracy over previous methods. Our work presents an original way of performing product demand forecasting in real-time in industry with highly accurate results which are much better than pre-existing demand forecasting models.

     

Forecasting models for Taiwanese tourism demand after allowance for Mainland China tourists visiting Taiwan

The tourism industry is an increasingly important national industry for Taiwan. Government policymakers and business managers pay close attention to the development of the tourism industry. In a rapidly changing environment that is influenced by numerous socioeconomic factors, the tourism industry must have an accurate method to forecast future tourism demand such that decision makers will be able to meet future challenges more effectively. Based on these concerns, this study proposes the SARIMA–GARCH model to analyze and forecast the tourism demand in Taiwan and compare the predictive power of this model and other forecasting models. The results provide a valuable reference for decision-makers in the tourism industry of Taiwan.     

Traffic flow forecasting by seasonal SVR with chaotic simulated annealing algorithm

Accurate forecasting of inter-urban traffic flow has been one of the most important issues globally in the research on road traffic congestion. However, the information of inter-urban traffic presents a challenging situation; the traffic flow forecasting involves a rather complex nonlinear data pattern, particularly during daily peak periods, traffic flow data reveals cyclic (seasonal) trend. In the recent years, the support vector regression model (SVR) has been widely used to solve nonlinear regression and time series problems. However, the applications of SVR models to deal with cyclic (seasonal) trend time series have not been widely explored. This investigation presents a traffic flow forecasting model that combines the seasonal support vector regression model with chaotic simulated annealing algorithm (SSVRCSA), to forecast inter-urban traffic flow. Additionally, a numerical example of traffic flow values from northern Taiwan is employed to elucidate the forecasting performance of the proposed SSVRCSA model. The forecasting results indicate that the proposed model yields more accurate forecasting results than the seasonal autoregressive integrated moving average (SARIMA), back-propagation neural network (BPNN) and seasonal Holt-Winters (SHW) models. Therefore, the SSVRCSA model is a promising alternative for forecasting traffic flow.