A new hybrid for improvement of auto-regressive integrated moving average models applying particle swarm optimization

A time series forecasting is an active research applied significantly in a variety of economics areas. Over the past three decades an auto-regressive integrated moving average (ARIMA) model, as one of the most important time series models, has been applied in financial markets forecasting. Recent researches in time series forecasting ARIMA models indicate some basic limitations which detract from their popularities for financial time series forecasting: One limitation of an ARIMA model is that it requires a large amount of historical data to generate an accurate result. Both theoretical and empirical findings suggest that combining different time series models may be an effective method of improving the predictive performances of data especially when the models in the ensemble are quite different. The main purpose of present paper is to combine the ARIMA model with the particle swarm optimization (PSO) model in order to improve and generate more accurate forecasting results. Under small data information, combining the PSO and ARIMA models performs better performance results compared to an ARIMA model itself. The proposed model is robust and it may be used as an alternative forecasting tool in economics areas.     

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.     

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.     

A spatio-temporal decomposition based deep neural network for time series forecasting

Spatio-temporal problems arise in a broad range of applications, such as climate science and transportation systems. These problems are challenging because of unique spatial, short-term and long-term patterns, as well as the curse of dimensionality. In this paper, we propose a deep learning framework for spatio-temporal forecasting problems. We explicitly design the neural network architecture for capturing various types of spatial and temporal patterns, and the model is robust to missing data. In a preprocessing step, a time series decomposition method is applied to separately feed short-term, long-term and spatial patterns into different components of the neural network. A fuzzy clustering method finds clusters of neighboring time series residuals, as these contain short-term spatial patterns. The first component of the neural network consists of multi-kernel convolutional layers which are designed to extract short-term features from clusters of time series data. Each convolutional kernel receives a single cluster of input time series. The output of convolutional layers is concatenated by trends and followed by convolutional-LSTM layers to capture long-term spatial patterns. To have a robust forecasting model when faced with missing data, a pretrained denoising autoencoder reconstructs the model’s output in a fine-tuning step. In experimental results, we evaluate the performance of the proposed model for the traffic flow prediction. The results show that the proposed model outperforms baseline and state-of-the-art neural network models.     

Image masking for crop yield forecasting using AVHRR NDVI time series imagery

One obstacle to successful modeling and prediction of crop yields using remotely sensed imagery is the identification of image masks. Image masking involves restricting an analysis to a subset of a region's pixels rather than using all of the pixels in the scene. Cropland masking, where all sufficiently cropped pixels are included in the mask regardless of crop type, has been shown to generally improve crop yield forecasting ability, but it requires the availability of a land cover map depicting the location of cropland. The authors present an alternative image masking technique, called yield-correlation masking, which can be used for the development and implementation of regional crop yield forecasting models and eliminates the need for a land cover map. The procedure requires an adequate time series of imagery and a corresponding record of the region's crop yields, and involves correlating historical, pixel-level imagery values with historical regional yield values. Imagery used for this study consisted of 1-km, biweekly AVHRR NDVI composites from 1989 to 2000. Using a rigorous evaluation framework involving five performance measures and three typical forecasting opportunities, yield-correlation masking is shown to have comparable performance to cropland masking across eight major U.S. region-crop forecasting scenarios in a 12-year cross-validation study. Our results also suggest that 11 years of time series AVHRR NDVI data may not be enough to estimate reliable linear crop yield models using more than one NDVI-based variable. A robust, but sub-optimal, all-subsets regression modeling procedure is described and used for testing, and historical United States Department of Agriculture crop yield estimates and linear trend estimates are used to gauge model performance.     

Modes decomposition method in fusion with robust random vector functional link network for crude oil price forecasting

This paper proposes a decomposition based method in fusion with the non-iterative approach for crude oil price forecasting. In this approach, the robust random vector functional link network (RVFLN), a non-iterative approach in fusion with the most efficient decomposition technique called variational mode decomposition (VMD) is proposed which is executed with two links — fixed assigned random weights and direct link from input to output, and the iterative learning process is not involved in its functioning which makes it faster in execution as compared to many existing techniques proposed for forecasting. The fusion of VMD and robust RVFLN called VMD-RVFLN is implemented for crude oil price forecasting where the crude oil price series is decomposed using VMD into a linear smoother series by extracting useful information and the decomposed modes pass through the robust RVFLN model which produces the final forecasting values. The analysis performed in the study approves its efficiency and reports improvement in forecasting accuracy and execution time as compared to some of the traditional iterative techniques like BPNN (back propagation neural network), ARIMA (auto-regressive integrated moving average), LSSVR (least squares support vector regression), ANFIS (adaptive neuro-fuzzy inference system), IT2FNN (interval type-2 fuzzy neural network) and RNN (recurrent neural network), etc. However, both ELM and RVFLN without modes decomposition fusion exhibit less execution time at the cost of reduction in prediction accuracy.     

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.     

A new forecasting scheme for evaluating long‐term prediction performances in supply chain management

Supply chain management (SCM) practitioners in inventory sites are often required to predict the future sales of products in order to meet customer demands and reduce inventory costs simultaneously. Although a variety of forecasting methods have been developed, many of them may not be used in practice for various reasons, such as insufficient viable information about sales and oversophisticated methods. In this paper, we provide a new forecasting scheme to evaluate long‐term prediction performances in SCM. Three well‐known forecasting methods for time series data—moving average (MA), autoregressive integrated MA, and smoothing spline—are considered. We also focus on two representative sales patterns, each of which is with and without a growth pattern, respectively. By applying the proposed scheme to various simulated and real datasets, this research aims to provide SCM practitioners with a general guideline for time series sales forecasting, so that they can easily understand what prediction performance measures and which forecasting method can be considered.     

A decision support system methodology for forecasting of time series based on soft computing

Exponential procedures are widely used as forecasting techniques for inventory control and business planning. A number of modifications to the generalized exponential smoothing (Holt-Winters) approach to forecasting univariate time series is presented, which have been adapted into a tool for decision support systems. This methodology unifies the phases of estimation and model selection into just one optimization framework which permits the identification of robust solutions. This procedure may provide forecasts from different versions of exponential smoothing by fitting the updated formulas of Holt-Winters and selects the best method using a fuzzy multicriteria approach. The elements of the set of local minima of the non-linear programming problems allow us to build the membership functions of the conflicting objectives. It is compared to other forecasting methods on the 111 series from the M-competition.     

Time Series Prediction With Genetic-Algorithm Designed Neural Networks: An Empirical Comparison With Modern Statistical Models

Neural networks whose architecture is determined by genetic algorithms outperform autoregressive integrated moving average forecasting models in six different time series examples. Refinements to the autoregressive integrated moving average model improve forecasting performance over standard ordinary least squares estimation by 8% to 13%. In contrast, neural networks achieve dramatic improvements of 10% to 40%. Additionally, neural networks give evidence of detecting patterns in data which remain hidden to the autoregression and moving average models. The consequent forecasting potential of neural networks makes them a very promising addition to the variety of techniques and methodologies used to anticipate future movements in time series.
     

Combining wavelet-based feature extractions with relevance vector machines for stock index forecasting

Abstract: The relevance vector machine (RVM) is a Bayesian version of the support vector machine, which with a sparse model representation has appeared to be a powerful tool for time-series forecasting. The RVM has demonstrated better performance over other methods such as neural networks or autoregressive integrated moving average based models. This study proposes a hybrid model that combines wavelet-based feature extractions with RVM models to forecast stock indices. The time series of explanatory variables are decomposed using some wavelet bases and the extracted time-scale features serve as inputs of an RVM to perform the non-parametric regression and forecasting. Compared with traditional forecasting models, our proposed method performs best. The root-mean-squared forecasting errors are significantly reduced.     

A new ARIMA-based neuro-fuzzy approach and swarm intelligence for time series forecasting

Time series forecasting is an important and widely interesting topic in the research of system modeling. We propose a new computational intelligence approach to the problem of time series forecasting, using a neuro-fuzzy system (NFS) with auto-regressive integrated moving average (ARIMA) models and a novel hybrid learning method. The proposed intelligent system is denoted as the NFS–ARIMA model, which is used as an adaptive nonlinear predictor to the forecasting problem. For the NFS–ARIMA, the focus is on the design of fuzzy If-Then rules, where ARIMA models are embedded in the consequent parts of If-Then rules. For the hybrid learning method, the well-known particle swarm optimization (PSO) algorithm and the recursive least-squares estimator (RLSE) are combined together in a hybrid way so that they can update the free parameters of NFS–ARIMA efficiently. The PSO is used to update the If-part parameters of the proposed predictor, and the RLSE is used to adapt the Then-part parameters. With the hybrid PSO–RLSE learning method, the NFS–ARIMA predictor may converge in fast learning pace with admirable performance. Three examples are used to test the proposed approach for forecasting ability. The results by the proposed approach are compared to other approaches. The performance comparison shows that the proposed approach performs appreciably better than the compared approaches. Through the experimental results, the proposed approach has shown excellent prediction performance.     

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.     

集成环境下的预测应用网络系统的设计与实现

本以青岛市委管理信息与辅助决策系统为背景,提出向一般计划管理人员的预测应用系统的开发设计原则：以通用、经典的预测方法为基础,以先进的计算机技术为手段,建立应用系统的集成环境,支持用户进行预测工作,重实效,重理解。并依此原则描述了集成环境下的预测应用网络系统的设计和实现。     

Integrated identification and robust control

A framework for integrated identification and control is presented. As part of this framework, frequency domain uncertainty bounds are derived for robust stability tests, a robust stability test for elliptical bounds is developed for SISO systems, a methodology for estimating controller performance is derived, and an optimal experiment design methodology for control-relevant identification is outlined. An example is presented to illustrate how the tools of the framework fit together.     

Enhanced stock price variation prediction via DOE and BPNN-based optimization

Stock price variation predictions are at the core of many research issues, and neural networks (NNs) are widely applied and were proven to be more efficient than time series forecasting for stock price forecasting. However, this type of research always determines the parameter settings of the NNs rationally through a trial-and-error methodology. This paper integrates design of experiment (DOE), Taguchi method, and back-propagation NN (BPNN) to construct a robust engine to further optimize the prediction accuracy under a robust DOE-based predictor. Adopting data from Taiwan Stock Exchange (TWSE), the technical analytical indexes and β value of the listed stocks of TWSE were computed. The research results indicated that the proposed approach can effectively improve the forecasting rate of stock price variations.     

基于一种时间序列模型的河流重金属污染浓度预测研究

水环境是一个充满不确定性的复杂巨系统,传统水质模型很难体现重金属污染物在河流中迁移的随机性,因此经典的时间序列模型——ARIMA模型被应用于河流重金属污染浓度的预测。实例分析证实,通过采用将荻得的最新数据不断地添加到用于模型设定的样本中,并再此基础上获得最近向前一个时期预测值的动态预测方法,ARIMA模型能够获得很好的预测表现,尤其是在充分考虑模型残差统计分布特征的情况下,采用具有学生t分布的模型预测更精确。     

Long memory time series forecasting by using genetic programming

Real-world time series have certain properties, such as stationarity, seasonality, linearity, among others, which determine their underlying behaviour. There is a particular class of time series called long-memory processes, characterized by a persistent temporal dependence between distant observations, that is, the time series values depend not only on recent past values but also on observations of much prior time periods. The main purpose of this research is the development, application, and evaluation of a computational intelligence method specifically tailored for long memory time series forecasting, with emphasis on many-step-ahead prediction. The method proposed here is a hybrid combining genetic programming and the fractionally integrated (long-memory) component of autoregressive fractionally integrated moving average (ARFIMA) models. Another objective of this study is the discovery of useful comprehensible novel knowledge, represented as time series predictive models. In this respect, a new evolutionary multi-objective search method is proposed to limit complexity of evolved solutions and to improve predictive quality. Using these methods allows for obtaining lower complexity (and possibly more comprehensible) models with high predictive quality, keeping run time and memory requirements low, and avoiding bloat and over-fitting. The methods are assessed on five real-world long memory time series and their performance is compared to that of statistical models reported in the literature. Experimental results show the proposed methods’ advantages in long memory time series forecasting.     

Robust design of integrated feedback and iterative learning control of a batch process based on a 2D Roesser system

To improve stability and convergence, feedback control is often incorporated with iterative learning control (ILC), resulting in feedback feed-forward ILC (FFILC). In this paper, a general form of FFILC is studied, comprising of two feedback controllers, a state feedback controller and a tracking error compensator, for the robustness and convergence along time direction, and an ILC for performance along the cycle direction. The integrated design of this FFILC scheme is transformed into a robust control problem of an uncertain 2D Roesser system. To describe the stability and convergence quantitatively along the time and the cycle direction, the concepts of robust stability and convergence along the two axes are introduced. A series of algorithms are established for the FFILC design. These algorithms allow the designer to balance and choose optimization objectives to meet the FFILC performance requirements. The applications to injection molding velocity control show the good effectiveness and feasibility of the proposed design methods.     

A hybrid optimized error correction system for time series forecasting

Time series forecasting is a challenging task in machine learning. Real world time series are often composed by linear and nonlinear structures which need to be mapped by some forecasting method. Linear methods such as autoregressive integrated moving average (ARIMA) and nonlinear methods such as artificial neural networks (ANNs) could be employed to handle such problems, however model misspecification hinders the forecasting process producing inaccurate models. Hybrid models based on error forecasting and combination can reduce the misspecification of single models and improve the accuracy of the system. This work proposes a hybrid system that is composed of three parts: a) linear modeling of the time series, b) nonlinear modeling of the error series, and c) combination of the forecasts using three distinct approaches. The system performs a search for the best parameters of the linear and nonlinear components, and of the combination approaches. Particle swarm optimization is used to find suitable architecture and weights. Experiments show that the proposed technique achieved promising results in time series forecasting.