A Time Series Short-Term Prediction Method Based on Multi-Granularity Event Matching and Alignment

Accurate forecasting of time series is crucial across various domains.Many prediction tasks rely on effectively segmenting,matching,and time series data alignment.For instance,regardless of time series with the same granularity,segmenting them into different granularity events can effectively mitigate the impact of varying time scales on prediction accuracy.However,these events of varying granularity frequently intersect with each other,which may possess unequal durations.Even minor differences can result in significant errors when matching time series with future trends.Besides,directly using matched events but unaligned events as state vectors in machine learning-based prediction models can lead to insufficient prediction accuracy.Therefore,this paper proposes a short-term forecasting method for time series based on a multi-granularity event,MGE-SP(multi-granularity event-based short-termprediction).First,amethodological framework for MGE-SP established guides the implementation steps.The framework consists of three key steps,including multi-granularity event matching based on the LTF(latest time first)strategy,multi-granularity event alignment using a piecewise aggregate approximation based on the compression ratio,and a short-term prediction model based on XGBoost.The data from a nationwide online car-hailing service in China ensures the method’s reliability.The average RMSE(root mean square error)and MAE(mean absolute error)of the proposed method are 3.204 and 2.360,lower than the respective values of 4.056 and 3.101 obtained using theARIMA(autoregressive integratedmoving average)method,as well as the values of 4.278 and 2.994 obtained using k-means-SVR(support vector regression)method.The other experiment is conducted on stock data froma public data set.The proposed method achieved an average RMSE and MAE of 0.836 and 0.696,lower than the respective values of 1.019 and 0.844 obtained using the ARIMA method,as well as the values of 1.350 and 1.172 obtained using the k-means-SVR method.

Deep Learning for Financial Time Series Prediction:A State-of-the-Art Review of Standalone and HybridModels

Financial time series prediction,whether for classification or regression,has been a heated research topic over the last decade.While traditional machine learning algorithms have experienced mediocre results,deep learning has largely contributed to the elevation of the prediction performance.Currently,the most up-to-date review of advanced machine learning techniques for financial time series prediction is still lacking,making it challenging for finance domain experts and relevant practitioners to determine which model potentially performs better,what techniques and components are involved,and how themodel can be designed and implemented.This review article provides an overview of techniques,components and frameworks for financial time series prediction,with an emphasis on state-of-the-art deep learning models in the literature from2015 to 2023,including standalonemodels like convolutional neural networks(CNN)that are capable of extracting spatial dependencies within data,and long short-term memory(LSTM)that is designed for handling temporal dependencies;and hybrid models integrating CNN,LSTM,attention mechanism(AM)and other techniques.For illustration and comparison purposes,models proposed in recent studies are mapped to relevant elements of a generalized framework comprised of input,output,feature extraction,prediction,and related processes.Among the state-of-the-artmodels,hybrid models like CNNLSTMand CNN-LSTM-AM in general have been reported superior in performance to stand-alone models like the CNN-only model.Some remaining challenges have been discussed,including non-friendliness for finance domain experts,delayed prediction,domain knowledge negligence,lack of standards,and inability of real-time and highfrequency predictions.The principal contributions of this paper are to provide a one-stop guide for both academia and industry to review,compare and summarize technologies and recent advances in this area,to facilitate smooth and informed implementation,and to highlight future research directions.

AFSTGCN:Prediction for multivariate time series using an adaptive fused spatial-temporal graph convolutional network

The prediction for Multivariate Time Series(MTS)explores the interrelationships among variables at historical moments,extracts their relevant characteristics,and is widely used in finance,weather,complex industries and other fields.Furthermore,it is important to construct a digital twin system.However,existing methods do not take full advantage of the potential properties of variables,which results in poor predicted accuracy.In this paper,we propose the Adaptive Fused Spatial-Temporal Graph Convolutional Network(AFSTGCN).First,to address the problem of the unknown spatial-temporal structure,we construct the Adaptive Fused Spatial-Temporal Graph(AFSTG)layer.Specifically,we fuse the spatial-temporal graph based on the interrelationship of spatial graphs.Simultaneously,we construct the adaptive adjacency matrix of the spatial-temporal graph using node embedding methods.Subsequently,to overcome the insufficient extraction of disordered correlation features,we construct the Adaptive Fused Spatial-Temporal Graph Convolutional(AFSTGC)module.The module forces the reordering of disordered temporal,spatial and spatial-temporal dependencies into rule-like data.AFSTGCN dynamically and synchronously acquires potential temporal,spatial and spatial-temporal correlations,thereby fully extracting rich hierarchical feature information to enhance the predicted accuracy.Experiments on different types of MTS datasets demonstrate that the model achieves state-of-the-art single-step and multi-step performance compared with eight other deep learning models.

Prediction of three-dimensional ocean temperature in the South China Sea based on time series gridded data and a dynamic spatiotemporal graph neural network

Ocean temperature is an important physical variable in marine ecosystems,and ocean temperature prediction is an important research objective in ocean-related fields.Currently,one of the commonly used methods for ocean temperature prediction is based on data-driven,but research on this method is mostly limited to the sea surface,with few studies on the prediction of internal ocean temperature.Existing graph neural network-based methods usually use predefined graphs or learned static graphs,which cannot capture the dynamic associations among data.In this study,we propose a novel dynamic spatiotemporal graph neural network(DSTGN)to predict threedimensional ocean temperature(3D-OT),which combines static graph learning and dynamic graph learning to automatically mine two unknown dependencies between sequences based on the original 3D-OT data without prior knowledge.Temporal and spatial dependencies in the time series were then captured using temporal and graph convolutions.We also integrated dynamic graph learning,static graph learning,graph convolution,and temporal convolution into an end-to-end framework for 3D-OT prediction using time-series grid data.In this study,we conducted prediction experiments using high-resolution 3D-OT from the Copernicus global ocean physical reanalysis,with data covering the vertical variation of temperature from the sea surface to 1000 m below the sea surface.We compared five mainstream models that are commonly used for ocean temperature prediction,and the results showed that the method achieved the best prediction results at all prediction scales.

Price Prediction of Seasonal Items Using Time Series Analysis

The price prediction task is a well-studied problem due to its impact on the business domain.There are several research studies that have been conducted to predict the future price of items by capturing the patterns of price change,but there is very limited work to study the price prediction of seasonal goods(e.g.,Christmas gifts).Seasonal items’prices have different patterns than normal items;this can be linked to the offers and discounted prices of seasonal items.This lack of research studies motivates the current work to investigate the problem of seasonal items’prices as a time series task.We proposed utilizing two different approaches to address this problem,namely,1)machine learning(ML)-based models and 2)deep learning(DL)-based models.Thus,this research tuned a set of well-known predictive models on a real-life dataset.Those models are ensemble learning-based models,random forest,Ridge,Lasso,and Linear regression.Moreover,two new DL architectures based on gated recurrent unit(GRU)and long short-term memory(LSTM)models are proposed.Then,the performance of the utilized ensemble learning and classic ML models are compared against the proposed two DL architectures on different accuracy metrics,where the evaluation includes both numerical and visual comparisons of the examined models.The obtained results show that the ensemble learning models outperformed the classic machine learning-based models(e.g.,linear regression and random forest)and the DL-based models.

TSCND:Temporal Subsequence-Based Convolutional Network with Difference for Time Series Forecasting

Time series forecasting plays an important role in various fields, such as energy, finance, transport, and weather. Temporal convolutional networks (TCNs) based on dilated causal convolution have been widely used in time series forecasting. However, two problems weaken the performance of TCNs. One is that in dilated casual convolution, causal convolution leads to the receptive fields of outputs being concentrated in the earlier part of the input sequence, whereas the recent input information will be severely lost. The other is that the distribution shift problem in time series has not been adequately solved. To address the first problem, we propose a subsequence-based dilated convolution method (SDC). By using multiple convolutional filters to convolve elements of neighboring subsequences, the method extracts temporal features from a growing receptive field via a growing subsequence rather than a single element. Ultimately, the receptive field of each output element can cover the whole input sequence. To address the second problem, we propose a difference and compensation method (DCM). The method reduces the discrepancies between and within the input sequences by difference operations and then compensates the outputs for the information lost due to difference operations. Based on SDC and DCM, we further construct a temporal subsequence-based convolutional network with difference (TSCND) for time series forecasting. The experimental results show that TSCND can reduce prediction mean squared error by 7.3% and save runtime, compared with state-of-the-art models and vanilla TCN.

A prediction comparison between univariate and multivariate chaotic time series

The methods to determine time delays and embedding dimensions in the phase space delay reconstruction of multivariate chaotic time series are proposed. Three nonlinear prediction methods of multivariate chaotic time series including local mean prediction, local linear prediction and BP neural networks prediction are considered. The simulation results obtained by the Lorenz system show that no matter what nonlinear prediction method is used, the prediction error of multivariate chaotic time series is much smaller than the prediction error of univariate time series, even if half of the data of univariate time series are used in multivariate time series. The results also verify that methods to determine the time delays and the embedding dimensions are correct from the view of minimizing the prediction error.

Local polynomial prediction method of multivariate chaotic time series and its application

To improve the prediction accuracy of chaotic time series, a new methodformed on the basis of local polynomial prediction is proposed. The multivariate phase spacereconstruction theory is utilized to reconstruct the phase space firstly, and on its basis, apolynomial function is applied to construct the prediction model, then the parameters of the modelaccording to the data matrix built with the embedding dimensions are estimated and a one-stepprediction value is calculated. An estimate and one-step prediction value is calculated. Finally,the mean squared root statistics are used to estimate the prediction effect. The simulation resultsobtained by the Lorenz system and the prediction results of the Shanghai composite index show thatthe local polynomial prediction errors of the multivariate chaotic time series are small and itsprediction accuracy is much higher than that of the univariate chaotic time series.

New prediction of chaotic time series based on local Lyapunov exponent

A new method of predicting chaotic time series is presented based on a local Lyapunov exponent, by quantitatively measuring the exponential rate of separation or attraction of two infinitely close trajectories in state space. After recon- structing state space from one-dimensional chaotic time series, neighboring multiple-state vectors of the predicting point are selected to deduce the prediction formula by using the definition of the locaI Lyapunov exponent. Numerical simulations are carded out to test its effectiveness and verify its higher precision over two older methods. The effects of the number of referential state vectors and added noise on forecasting accuracy are also studied numerically.

Fault Prediction Based on Dynamic Model and Grey Time Series Model in Chemical Processes

This paper combines grey model with time series model and then dynamic model for rapid and in-depth fault prediction in chemical processes. Two combination methods are proposed. In one method, historical data is introduced into the grey time series model to predict future trend of measurement values in chemical process. These predicted measurements are then used in the dynamic model to retrieve the change of fault parameters by model based diagnosis algorithm. In another method, historical data is introduced directly into the dynamic model to retrieve historical fault parameters by model based diagnosis algorithm. These parameters are then predicted by the grey time series model. The two methods are applied to a gravity tank example. The case study demonstrates that the first method is more accurate for fault prediction.

Time series prediction using wavelet process neural network

In the real world, the inputs of many complicated systems are time-varying functions or processes. In order to predict the outputs of these systems with high speed and accuracy, this paper proposes a time series prediction model based on the wavelet process neural network, and develops the corresponding learning algorithm based on the expansion of the orthogonal basis functions. The effectiveness of the proposed time series prediction model and its learning algorithm is proved by the Macke-Glass time series prediction, and the comparative prediction results indicate that the proposed time series prediction model based on the wavelet process neural network seems to perform well and appears suitable for using as a good tool to predict the highly complex nonlinear time series.

Application of uncertainty reasoning based on cloud model in time series prediction

Time series prediction has been successfully used in several application areas, such as meteoro-logical forecasting, market prediction, network traffic forecasting, etc. , and a number of techniques have been developed for modeling and predicting time series. In the traditional exponential smoothing method, a fixed weight is assigned to data history, and the trend changes of time series are ignored. In this paper, an uncertainty reasoning method, based on cloud model, is employed in time series prediction, which uses cloud logic controller to adjust the smoothing coefficient of the simple exponential smoothing method dynamically to fit the current trend of the time series. The validity of this solution was proved by experiments on various data sets.

Time series online prediction algorithm based on least squares support vector machine

Deficiencies of applying the traditional least squares support vector machine （LS-SVM） to time series online prediction were specified. According to the kernel function matrix＇s property and using the recursive calculation of block matrix, a new time series online prediction algorithm based on improved LS-SVM was proposed. The historical training results were fully utilized and the computing speed of LS-SVM was enhanced. Then, the improved algorithm was applied to timc series online prediction. Based on the operational data provided by the Northwest Power Grid of China, the method was used in the transient stability prediction of electric power system. The results show that, compared with the calculation time of the traditional LS-SVM（75 1 600 ms）, that of the proposed method in different time windows is 40-60 ms, proposed method is above 0.8. So the improved method is online prediction. and the prediction accuracy（normalized root mean squared error） of the better than the traditional LS-SVM and more suitable for time series online prediction.

Prediction of chaotic time series based on modified minimax probability machine regression

Long-term prediction of chaotic time series is very difficult,for the Chaos restricts predictability.in this paper a new method is studied to model and predict chaotic time series based on minimax probability machine regression （MPMR）. Since the positive global Lyapunov exponents lead the errors to increase exponentially in modelling the chaotic time series, a weighted term is introduced to compensate a cost function. Using mean square error （MSE） and absolute error （AE） as a criterion, simulation results show that the proposed method is more effective and accurate for multistep prediction. It can identify the system characteristics quite well and provide a new way to make long-term predictions of the chaotic time series.

Time Series Models for Short Term Prediction of the Incidence of Japanese Encephalitis in Xianyang City, P R China

Objective To construct a model of Seasonal Autoregressive Integrated Moving Average （SARIMA） for forecasting the epidemic of Japanese encephalitis （JE） in Xianyang, Shaanxi, China, and provide valuable reference information for JE control and prevention. Methods Theoretically epidemiologic study was employed in the research process. Monthly incidence data on JE for the period from Jan 2005 to Sep 2014 were obtained from a passive surveillance system at the Center for Diseases Prevention and Control in Xianyang, Shaanxi province. An optimal SARIMA model was developed for JE incidence from 2005 to 2013 with the Box and Jenkins approach. This SARIMA model could predict JE incidence for the year 2014 and 2015. Results SARIMA （1, 1, 1） （2, 1, 1）12 was considered to be the best model with the lowest Bayesian information criterion, Akaike information criterion, Mean Absolute Error values, the highest R2, and a lower Mean Absolute Percent Error. SARIMA （1, 1, 1） （2, 1, 1）12 was stationary and accurate for predicting JE incidence in Xianyang. The predicted incidence, around 0.3/100 000 from June to August in 2014 with low errors, was higher compared with the actual incidence. Therefore, SARIMA （1, 1, 1） （2, 1, 1）12 appeared to be reliable and accurate and could be applied to incidence prediction. Conclusions The proposed prediction model could provide clues to early identification of the JE incidence that is increased abnormally （≥0.4/100 000）. According to the predicted results in 2014, the JE incidence in Xianyang will decline slightly and reach its peak from June to August.The authors wish to thank the staff from the CDCs from 13 counties of Xianyang, Shaanxi province, China, for their contribution to Japanese encephalitis cases reporting.

STUDY ON THE PREDICTION METHOD OF LOW-DIMENSION TIME SERIES THAT ARISE FROM THE INTRINSIC NONLINEAR DYNAMICS

The prediction methods and its applications of the nonlinear dynamic systems determined from chaotic time series of low-dimension are discussed mainly. Based on the work of the foreign researchers, the chaotic time series in the phase space adopting one kind of nonlinear chaotic model were reconstructed. At first, the model parameters were estimated by using the improved least square method. Then as the precision was satisfied, the optimization method was used to estimate these parameters. At the end by using the obtained chaotic model, the future data of the chaotic time series in the phase space was predicted. Some representative experimental examples were analyzed to testify the models and the algorithms developed in this paper. ne results show that if the algorithms developed here are adopted, the parameters of the corresponding chaotic model will be easily calculated well and true. Predictions of chaotic series in phase space make the traditional methods change from outer iteration to interpolations. And if the optimal model rank is chosen, the prediction precision will increase notably. Long term superior predictability of nonlinear chaotic models is proved to be irrational and unreasonable.

Discussion About Nonlinear Time Series Prediction Using Least Squares Support Vector Machine

The least squares support vector machine (LS-SVM) is used to study the nonlinear time series prediction. First, the parameter gamma and multi-step prediction capabilities of the LS-SVM network are discussed. Then we employ clustering method in the model to prune the number of the support values.. The learning rate and the capabilities of filtering noise for LS-SVM are all greatly improved.

Chaotic time series prediction using fuzzy sigmoid kernel-based support vector machines

Support vector machines （SVM） have been widely used in chaotic time series predictions in recent years. In order to enhance the prediction efficiency of this method and implement it in hardware, the sigmoid kernel in SVM is drawn in a more natural way by using the fuzzy logic method proposed in this paper. This method provides easy hardware implementation and straightforward interpretability. Experiments on two typical chaotic time series predictions have been carried out and the obtained results show that the average CPU time can be reduced significantly at the cost of a small decrease in prediction accuracy, which is favourable for the hardware implementation for chaotic time series prediction.

The improved local linear prediction of chaotic time series

Based on the Bayesian information criterion, this paper proposes the improved local linear prediction method to predict chaotic time series. This method uses spatial correlation and temporal correlation simultaneously. Simulation results show that the improved local linear prediction method can effectively make multi-step and one-step prediction of chaotic time series and the multi-step prediction performance and one-step prediction accuracy of the improved local linear prediction method are superior to those of the traditional local linear prediction method.

Generalized unscented Kalman filtering based radial basis function neural network for the prediction of ground radioactivity time series with missing data

On the assumption that random interruptions in the observation process are modeled by a sequence of independent Bernoulli random variables, we firstly generalize two kinds of nonlinear filtering methods with random interruption failures in the observation based on the extended Kalman filtering （EKF） and the unscented Kalman filtering （UKF）, which were shortened as GEKF and CUKF in this paper, respectively. Then the nonlinear filtering model is established by using the radial basis function neural network （RBFNN） prototypes and the network weights as state equation and the output of RBFNN to present the observation equation. Finally, we take the filtering problem under missing observed data as a special case of nonlinear filtering with random intermittent failures by setting each missing data to be zero without needing to pre-estimate the missing data, and use the GEKF-based RBFNN and the GUKF-based RBFNN to predict the ground radioactivity time series with missing data. Experimental results demonstrate that the prediction results of GUKF-based RBFNN accord well with the real ground radioactivity time series while the prediction results of GEKF-based RBFNN are divergent.