Recursive prediction for long term time series forecasting using advanced models

There exists a wide range of paradigms, and a high number of different methodologies that are applied to the problem of time series prediction. Most of them are presented as a modified function approximation problem using input/output data, in which the input data are expanded using values of the series at previous steps. Thus, the model obtained normally predicts the value of the series at a time (t+h) using previous time steps (t-τ₁),(t-τ₂),…,(t-τ_n). Nevertheless, learning a model for long term time series prediction might be seen as a more complicated task, since it might use its own outputs as inputs for long term prediction (recursive prediction). This paper presents the utility of two different methodologies, the TaSe fuzzy TSK model and the least-squares SVMs, to solve the problem of long term time series prediction using recursive prediction. This work also introduces some techniques that upgrade the performance of those advanced one-step-ahead models (and in general of any one-step-ahead model), where they are used recursively for long term time series prediction.     

Swarm-based translation-invariant morphological prediction method for financial time series forecasting

In this paper, we present a method to overcome the random walk (RW) dilemma for financial time series forecasting, called swarm-based translation-invariant morphological prediction (STMP) method. It consists of a hybrid model composed of a modular morphological neural network (MMNN) combined with a particle swarm optimizer (PSO), which searches for the best time lags to optimally describe the time series phenomenon, as well as estimates the initial (sub-optimal) parameters of the MMNN (weights, architecture and number of modules). An additional optimization is performed with each particle of the PSO population (a distinct MMNN) using the back-propagation (BP) algorithm. After the MMNN parameters adjustment, we use a behavioral statistical test and a phase fix procedure to adjust time phase distortions observed in financial time series. Finally, we conduct an experimental analysis with the proposed method using four real world stock market time series, where five well-known performance metrics and a fitness function are used to assess the prediction performance. The obtained results are compared with those generated by classical models presented in the literature.     

基于序列分解的复杂系统的时序预测方法

现实中的时序数据，往往取自于复杂系统，表现出长记忆效应与短时不规则波动同时并存。传统的时序数据的分析和预测方法一般对不同层次的影响不加以区分，而是为其建立一个统一的模型，这使得在对复杂系统建模时需要用大量的参数予以表征，影响预测效率与精度。为此采用新的方法，将序列数据本身进行多平滑因子分解，对分解后的序列进行多尺度的采样并分别建模、预测，最后将结果整合。该方法应用于股票的实验表明，即使对起伏波动很大的时间序列，也能够得到较好的预测结果。     

Integration of similarity measurement and dynamic SVM for electrically evoked potentials prediction in visual prostheses research

Electrical evoked potentials (EEPs) time series prediction is a novel topic concentrating on reducing the cost of the visual prostheses research. Support vector machine (SVM), a superior neural network algorithm, is a powerful tool for time series forecasting but is insensitive to multivariate analysis. Meanwhile, similarity measurement (SM), a key technology in case-based reasoning, has been applied in a wide variety of fields but is only limited to the point-to-point computation. This paper firstly attempts to take the advantages of SM and SVM to generate a high performance EEPs predictor. Four independent SM metrics, i.e. fuzzy SM, numeric SM, textual SM and interval SM are employed to calculate the similarities between input variables (including electrical stimulation parameter and spatial parameter) and corresponding experimental values. Then SVM is utilized to predict EEPs behavior in terms of the temporal input. Furthermore, we add the similarities and temporal weights into SVM to indicate that recent data from similar experimental cases could provide more information than distant data from dissimilar ones. Due to the dynamic property, the new SVM is called dynamic SVM, i.e. DSVM and the predictor is named SM-DSVM. How to implement the hybrid predictor with grid-search for parameter optimization is illustrated in detail. In the empirical comparison, the predictive performances on 30 hold-out data are used to make comparisons between SM-DSVM and other comparative predictors. Empirical results show that SM-DSVM is feasible and validated for EEPs prediction in visual prostheses research.     

基于证据理论的模糊时间序列预测模型

在分析经典模糊时间序列预测模型的基础上,指出了传统的模型不能处理多因素的情形;然后分析并改进了证据理论中关于证据合成的方法,提出了基于证据理论的多因素模糊时间序列预测模型;最后用1997年～2006年10年间的上海股指数据对所提出的模型进行了实践检验,实验结果表明该模型是可行的,其预测效果优于所参照的预测模型.     

Partitions based computational method for high-order fuzzy time series forecasting

In this paper, we present a computational method of forecasting based on multiple partitioning and higher order fuzzy time series. The developed computational method provides a better approach to enhance the accuracy in forecasted values. The objective of the present study is to establish the fuzzy logical relations of different order for each forecast. Robustness of the proposed method is also examined in case of external perturbation that causes the fluctuations in time series data. The general suitability of the developed model has been tested by implementing it in forecasting of student enrollments at University of Alabama. Further it has also been implemented in the forecasting the market price of share of State Bank of India (SBI) at Bombay Stock Exchange (BSE), India. In order to show the superiority of the proposed model over few existing models, the results obtained have been compared in terms of mean square and average forecasting errors.     

Fuzzy based trend mapping and forecasting for time series data

The study demonstrates the superiority of fuzzy based methods for non-stationary, non-linear time series. Study is based on unequal length fuzzy sets and uses IF-THEN based fuzzy rules to capture the trend prevailing in the series. The proposed model not only predicts the value but can also identify the transition points where the series may change its shape and is ready to include subject expert’s opinion to forecast. The series is tested on three different types of data: enrolment for Alabama university, sales volume of a chemical company and Gross domestic capital of India: the growth curve. The model is tested on both kind of series: with and without outliers. The proposed model provides an improved prediction with lesser MAPE (mean average percentage error) for all the series tested.     

Construction of a new BRB based model for time series forecasting

It is important to predict the future behavior of complex systems. Currently there are no effective methods to solve time series forecasting problem by using the quantitative and qualitative information. Therefore, based on belief rule base (BRB), this paper focuses on developing a new model that can deal with the problem. Although it is difficult to obtain accurately and completely quantitative information, some qualitative information can be collected and represented by a BRB. As such, a new BRB based forecasting model is proposed when the quantitative and qualitative information exist simultaneously. The performance of the proposed model depends on the structure and belief degrees of BRB simultaneously. Moreover, the structure is determined by the delay step. In order to obtain the appropriate delay step using the available information, a model selection criterion is defined according to Akaike's information criterion (AIC). Based on the proposed model selection criterion and the optimal algorithm for training the belief degrees, an algorithm for constructing the BRB based forecasting model is developed. Experimental results show that the constructed BRB based forecasting model can not only predict the time series accurately, but also has the appropriate structure.     

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.     

A clustering based forecasting algorithm for multivariable fuzzy time series using linear combinations of independent variables

There are two popular types of forecasting algorithms for fuzzy time series (FTS). One is based on intervals of universal sets of independent variables and the other is based on fuzzy clustering algorithms. Clustering based FTS algorithms are preferred since role and optimal length of intervals are not clearly understood. Therefore data of each variable are individually clustered which requires higher computational time. Fuzzy Logical Relationships (FLRs) are used in existing FTS algorithms to relate input and output data. High number of clusters and FLRs are required to establish precise input/output relations which incur high computational time. This article presents a forecasting algorithm based on fuzzy clustering (CFTS) which clusters vectors of input data instead of clustering data of each variable separately and uses linear combinations of the input variables instead of the FLRs. The cluster centers handle fuzziness and ambiguity of the data and the linear parts allow the algorithm to learn more from the available information. It is shown that CFTS outperforms existing FTS algorithms with considerably lower testing error and running time.     

A big data framework for stock price forecasting using fuzzy time series

Multimedia Tools and Applications - Stock price forecasting is the most difficult field owing to irregularities. Therefore, the stock price forecasting and recommendation is an extremely...     

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.     

VTG schemes for using back propagation for multivariate time series prediction

This research proposes the three schemes of estimating and adding mid-terms to multivariate time series. In this research, the back propagation is adopted as the approach to multivariate time series prediction. It is traditionally designed for the task with the two models: separated model and combined model. In the proposed version of time series prediction systems, the mid-term estimator is added as the additional module to the traditional version. It is validated empirically that the three VTG (Virtual Term Generation) schemes are effective on using the back propagation for multivariate time series prediction on the four test data sets: three artificial one and a real test one.     

Forecasting models for prediction in time series

This paper presents the study of three forecasting models??a multilayer perceptron, a support vector machine, and a hierarchical model. The hierarchical model is made up of a self-organizing map and a support vector machine??the latter on top of the former. The models are trained and assessed on a time series of a Brazilian stock market fund. The results from the experiments show that the performance of the hierarchical model is better than that of the support vector machine, and much better than that of the multilayer perceptron.     

Empirical Mode Decomposition based ensemble deep learning for load demand time series forecasting

Load demand forecasting is a critical process in the planning of electric utilities. An ensemble method composed of Empirical Mode Decomposition (EMD) algorithm and deep learning approach is presented in this work. For this purpose, the load demand series were first decomposed into several intrinsic mode functions (IMFs). Then a Deep Belief Network (DBN) including two restricted Boltzmann machines (RBMs) was used to model each of the extracted IMFs, so that the tendencies of these IMFs can be accurately predicted. Finally, the prediction results of all IMFs can be combined by either unbiased or weighted summation to obtain an aggregated output for load demand. The electricity load demand data sets from Australian Energy Market Operator (AEMO) are used to test the effectiveness of the proposed EMD-based DBN approach. Simulation results demonstrated attractiveness of the proposed method compared with nine forecasting methods.     

空分过程变量预测的多变量时间序列分析方法

氮塞是空分过程的常见故障,粗氩塔冷凝器出口氩气含氩量是工业现场中指示氮塞是否发生的关键变量,对该变量进行准确的预测可以使氮塞故障的报警时间提前.本文采用多变量时间序列相空间重构的方法,建立了粗氩塔冷凝器出口氩气含氩量和其它过程变量之间的一步线性回归预测模型,以迭代方式获得多步预测的结果,并利用滑动窗口实现了模型参数的在线修正.通过某钢铁公司空分装置实际数据的建模与仿真,分析了相空间重构时嵌入维数以及预测步数的选取对最终预测结果的影响,即预测均方误差与嵌入维数成反比,与预测步数成正比.仿真结果同时表明,本文建立的模型能够较为准确地对空分过程关键变量进行预测,预测提前时间在4～5分钟之间.     

Yield estimation and forecasting for winter wheat in Hungary using time series of MODIS data

Wheat is one of the most important crops in Hungary, which represents approximately 20% of the entire agricultural area of the country, and about 40% of cereals. A robust yield method has been improved for estimating and forecasting wheat yield in Hungary in the period of 2003–2015 using normalized difference vegetation index (NDVI) derived from the data of the Moderate Resolution Imaging Spectroradiometer. Estimation was made at the end of June – it is generally the beginning of harvest of winter wheat in Hungary – while the forecasts were performed 1–7 weeks earlier. General yield unified robust reference index (GYURRI) vegetation index was calculated each year using different curve-fitting methods to the NDVI time series. The correlation between GYURRI and country level yield data gave correlation coefficient (r) of 0.985 for the examined 13 years in the case of estimation. Simulating a quasi-operative yield estimation process, 10 years’ (2006–2015) yield data was estimated. The differences between the estimated and actual yield data provided by the Hungarian Central Statistical Office were less than 5%, the average difference was 2.5%. In the case of forecasting, these average differences calculated approximately 2 and 4 weeks before the beginning of harvest season were 4.5% and 6.8%, respectively. We also tested the yield estimation procedure for smaller areas, for the 19 counties (Nomenclature of Territorial Units for Statistics-3 level) of Hungary. We found that, the relationship between GYURRI and the county level yield data had r of 0.894 for the years 2003–2014, and by simulating the quasi-operative forecast for 2015, the resulting 19 county average yield values differed from the actual yield as much as 8.7% in average.     

A computer program for time series forecasting using single and double exponential smoothing techniques

This paper presents a microcomputer program for time series forecasting. The program has been developed in GW-BASIC for Zenith 150 microcomputers which are IBM PC compatible. It utilizes Single exponential smoothing, Adaptive-response-rate single exponential smoothing, and Brown's double exponential smoothing methods to forecast the future values of a given time series. The program produces plots of the original time series and forecasted series as well as forecasting errors. It computes 90% and 95% confidence intervals for forecasted values and calculates the following statistics: Mean squared error, Mean absolute percentage error, Mean absolute error, Durbin-Watson statistic, and Theil's U statistic.     

A moving-average filter based hybrid ARIMA–ANN model for forecasting time series data

A suitable combination of linear and nonlinear models provides a more accurate prediction model than an individual linear or nonlinear model for forecasting time series data originating from various applications. The linear autoregressive integrated moving average (ARIMA) and nonlinear artificial neural network (ANN) models are explored in this paper to devise a new hybrid ARIMA–ANN model for the prediction of time series data. Many of the hybrid ARIMA–ANN models which exist in the literature apply an ARIMA model to given time series data, consider the error between the original and the ARIMA-predicted data as a nonlinear component, and model it using an ANN in different ways. Though these models give predictions with higher accuracy than the individual models, there is scope for further improvement in the accuracy if the nature of the given time series is taken into account before applying the models. In the work described in this paper, the nature of volatility was explored using a moving-average filter, and then an ARIMA and an ANN model were suitably applied. Using a simulated data set and experimental data sets such as sunspot data, electricity price data, and stock market data, the proposed hybrid ARIMA–ANN model was applied along with individual ARIMA and ANN models and some existing hybrid ARIMA–ANN models. The results obtained from all of these data sets show that for both one-step-ahead and multistep-ahead forecasts, the proposed hybrid model has higher prediction accuracy.