A Hybrid Neural Network and Box-Jenkins Models for Time Series Forecasting

Time series forecasting plays a significant role in numerous applications,including but not limited to,industrial planning,water consumption,medical domains,exchange rates and consumer price index.The main problem is insufficient forecasting accuracy.The present study proposes a hybrid forecastingmethods to address this need.The proposed method includes three models.The first model is based on the autoregressive integrated moving average(ARIMA)statistical model;the second model is a back propagation neural network(BPNN)with adaptive slope and momentum parameters;and the thirdmodel is a hybridization between ARIMA and BPNN(ARIMA/BPNN)and artificial neural networks and ARIMA(ARIMA/ANN)to gain the benefits of linear and nonlinearmodeling.The forecasting models proposed in this study are used to predict the indices of the consumer price index(CPI),and predict the expected number of cancer patients in the Ibb Province in Yemen.Statistical standard measures used to evaluate the proposed method include(i)mean square error,(ii)mean absolute error,(iii)root mean square error,and(iv)mean absolute percentage error.Based on the computational results,the improvement rate of forecasting the CPI dataset was 5%,71%,and 4%for ARIMA/BPNN model,ARIMA/ANN model,and BPNN model respectively;while the result for cancer patients’dataset was 7%,200%,and 19%for ARIMA/BPNNmodel,ARIMA/ANN model,and BPNNmodel respectively.Therefore,it is obvious that the proposed method reduced the randomness degree,and the alterations affected the time series with data non-linearity.The ARIMA/ANN model outperformed each of its components when it was applied separately in terms of increasing the accuracy of forecasting and decreasing the overall errors of forecasting.

Selection of Heteroscedastic Models: A Time Series Forecasting Approach

To overcome the weaknesses of in-sample model selection, this study adopted out-of-sample model selection approach for selecting models with improved forecasting accuracies and performances. Daily closing share prices were obtained from Diamond Bank and Fidelity Bank as listed in the Nigerian Stock Exchange spanning from January 3, 2006 to December 30, 2016. Thus, a total of 2713 observations were explored and were divided into two portions. The first which ranged from January 3, 2006 to November 24, 2016, comprising 2690 observations, was used for model formulation. The second portion which ranged from November 25, 2016 to December 30, 2016, consisting of 23 observations, was used for out-of-sample forecasting performance evaluation. Combined linear (ARIMA) and Nonlinear (GARCH-type) models were applied on the returns series with respect to normal and student-t distributions. The findings revealed that ARIMA (2,1,1)-EGARCH (1,1)-norm and ARIMA (1,1,0)-EGARCH (1,1)-norm models selected based on minimum predictive errors throughout-of-sample approach outperformed ARIMA (2,1,1)-GARCH (2,0)-std and ARIMA (1,1,0)-EGARCH (1,1)-std model chosen through in-sample approach. Therefore, it could be deduced that out-of-sample model selection approach was suitable for selecting models with improved forecasting accuracies and performances.

TIME SERIES NEURAL NETWORK MODEL FOR HYDROLOGIC FORECASTING

Time series analysis plays an important role in hydrologic forecasting,while the key to this analysis is to establish a proper model.This paper presents a time series neural network model with back propagation procedure for hydrologic forecasting.Free from the disadvantages of previous models,the model can be parallel to operate information flexibly and rapidly.It excels in the ability of nonlinear mapping and can learn and adjust by itself,which gives the model a possibility to describe the complex nonlinear hydrologic process.By using directly a training process based on a set of previous data, the model can forecast the time series of stream flow.Moreover,two practical examples were used to test the performance of the time series neural network model.Results confirm that the model is efficient and feasible.

Time Series Analysis and Prediction of COVID-19 Pandemic Using Dynamic Harmonic Regression Models

Rapidly spreading COVID-19 virus and its variants, especially in metropolitan areas around the world, became a major health public concern. The tendency of COVID-19 pandemic and statistical modelling represents an urgent challenge in the United States for which there are few solutions. In this paper, we demonstrate combining Fourier terms for capturing seasonality with ARIMA errors and other dynamics in the data. Therefore, we have analyzed 156 weeks COVID-19 dataset on national level using Dynamic Harmonic Regression model, including simulation analysis and accuracy improvement from 2020 to 2023. Most importantly, we provide new advanced pathways which may serve as targets for developing new solutions and approaches.

Multi-factor high-order intuitionistic fuzzy timeseries forecasting model

Fuzzy sets theory cannot describe the neutrality degreeof data, which has largely limited the objectivity of fuzzy time seriesin uncertain data forecasting. With this regard, a multi-factor highorderintuitionistic fuzzy time series forecasting model is built. Inthe new model, a fuzzy clustering algorithm is used to get unequalintervals, and a more objective technique for ascertaining membershipand non-membership functions of the intuitionistic fuzzy setis proposed. On these bases, forecast rules based on multidimensionalintuitionistic fuzzy modus ponens inference are established.Finally, contrast experiments on the daily mean temperature ofBeijing are carried out, which show that the novel model has aclear advantage of improving the forecast accuracy.

Short and Long-Term Time Series Forecasting Stochastic Analysis for Slow Dynamic Processes

This paper intends to develop suitable methods to provide likely scenarios in order to support decision making for slow dynamic processes such as the underlying of agribusiness. A new method to analyze the short- and long-term time series forecast and to model the behavior of the underlying process using nonlinear artificial neural networks (ANN) is presented. The algorithm can effectively forecast the time-series data by stochastic analysis (Monte Carlo) of its future behavior using fractional Gaussian noise (fGn). The algorithm was used to forecast country risk time series for several countries, both for short term that is 30 days ahead and long term 350 days ahead scenarios.

CT-NET: A Novel Convolutional Transformer-Based Network for Short-Term Solar Energy Forecasting Using Climatic Information

Photovoltaic(PV)systems are environmentally friendly,generate green energy,and receive support from policies and organizations.However,weather fluctuations make large-scale PV power integration and management challenging despite the economic benefits.Existing PV forecasting techniques(sequential and convolutional neural networks(CNN))are sensitive to environmental conditions,reducing energy distribution system performance.To handle these issues,this article proposes an efficient,weather-resilient convolutional-transformer-based network(CT-NET)for accurate and efficient PV power forecasting.The network consists of three main modules.First,the acquired PV generation data are forwarded to the pre-processing module for data refinement.Next,to carry out data encoding,a CNNbased multi-head attention(MHA)module is developed in which a single MHA is used to decode the encoded data.The encoder module is mainly composed of 1D convolutional and MHA layers,which extract local as well as contextual features,while the decoder part includes MHA and feedforward layers to generate the final prediction.Finally,the performance of the proposed network is evaluated using standard error metrics,including the mean squared error(MSE),root mean squared error(RMSE),and mean absolute percentage error(MAPE).An ablation study and comparative analysis with several competitive state-of-the-art approaches revealed a lower error rate in terms of MSE(0.0471),RMSE(0.2167),and MAPE(0.6135)over publicly available benchmark data.In addition,it is demonstrated that our proposed model is less complex,with the lowest number of parameters(0.0135 M),size(0.106 MB),and inference time(2 ms/step),suggesting that it is easy to integrate into the smart grid.

Comparison of performance of statistical models in forecasting monthly streamflow of Kizil River,China

This paper presents the application of autoregressive integrated moving average （ARIMA）, seasonal ARIMA （SARIMA）, and Jordan-Elman artificial neural networks （ANN） models in forecasting the monthly streamflow of the Kizil River in Xinjiang, China. Two different types of monthly streamflow data （original and deseasonalized data） were used to develop time series and Jordan-Elman ANN models using previous flow conditions as predictors. The one-month-ahead forecasting performances of all models for the testing period （1998-2005） were compared using the average monthly flow data from the Kalabeili gaging station on the Kizil River. The Jordan-Elman ANN models, using previous flow conditions as inputs, resulted in no significant improvement over time series models in one-month-ahead forecasting. The results suggest that the simple time series models （ARIMA and SARIMA） can be used in one-month-ahead streamflow forecasting at the study site with a simple and explicit model structure and a model performance similar to the Jordan-Elman ANN models.

Modeling and Forecasting of Carbon Dioxide Emissions in Bangladesh Using Autoregressive Integrated Moving Average (ARIMA) Models

In the present paper, different Autoregressive Integrated Moving Average (ARIMA) models were developed to model the carbon dioxide emission by using time series data of forty-four years from 1972-2015. The performance of these developed models was assessed with the help of different selection measure criteria and the model having minimum value of these criteria considered as the best forecasting model. Based on findings, it has been observed that out of different ARIMA models, ARIMA (0, 2, 1) is the best fitted model in predicting the emission of carbon dioxide in Bangladesh. Using this best fitted model, the forecasted value of carbon dioxide emission in Bangladesh, for the year 2016, 2017 and 2018 as obtained from ARIMA (0, 2, 1) was obtained as 83.94657 Metric Tons, 89.90464 Metric Tons and 96.28557 Metric Tons respectively.

SeisGuard: A Software Platform to Establish Automatically an Earthquake Forecasting Model

SeisGuard, a system for analyzing earthquake precursory data, is a software platform to search for earthquake precursory information by processing geophysical data from different sources to establish automatically an earthquake forecasting model. The main function of this system is to analyze and process the deformation, fluid, electromagnetic and other geophysical field observing data from ground-based observation, as well as space-based observation. Combined station and earthquake distributions, geological structure and other information, this system can provide a basic software platform for earthquake forecasting research based on spatiotemporal fusion. The hierarchical station tree for data sifting and the interaction mode have been innovatively developed in this SeisGuard system to improve users’ working efficiency. The data storage framework designed according to the characteristics of different time series can unify the interfaces of different data sources, provide the support of data flow, simplify the management and usage of data, and provide foundation for analysis of big data. The final aim of this development is to establish an effective earthquake forecasting model combined all available information from ground-based observations to space-based observations.

Comprehensive applicability evaluation of four precipitation products at multiple spatiotemporal scales in Northwest China

Precipitation plays a crucial role in the water cycle of Northwest China.Obtaining accurate precipitation data is crucial for regional water resource management,hydrological forecasting,flood control and drought relief.Currently,the applicability of multi-source precipitation products for long time series in Northwest China has not been thoroughly evaluated.In this study,precipitation data from 183 meteorological stations in Northwest China from 1979 to 2020 were selected to assess the regional applicability of four precipitation products(the fifth generation of European Centre for Medium-Range Weather Forecasts(ECMWF)atmospheric reanalysis of the global climate(ERA5),Global Precipitation Climatology Centre(GPCC),Climatic Research Unit gridded Time Series Version 4.07(CRU TS v4.07,hereafter CRU),and Tropical Rainfall Measuring Mission(TRMM))based on the following statistical indicators:correlation coefficient,root mean square error(RMSE),relative bias(RB),mean absolute error(MAE),probability of detection(POD),false alarm ratio(FAR),and equitable threat score(ETS).The results showed that precipitation in Northwest China was generally high in the east and low in the west,and exhibited an increasing trend from 1979 to 2020.Compared with the station observations,ERA5 showed a larger spatial distribution difference than the other products.The overall overestimation of multi-year average precipitation was approximately 200.00 mm and the degree of overestimation increased with increasing precipitation intensity.The multi-year average precipitation of GPCC and CRU was relatively close to that of station observations.The trend of annual precipitation of TRMM was overestimated in high-altitude regions and the eastern part of Lanzhou with more precipitation.At the monthly scale,GPCC performed well but underestimated precipitation in the Tarim Basin(RB=-4.11%),while ERA5 and TRMM exhibited poor accuracy in high-altitude regions.ERA5 had a large bias(RB≥120.00%)in winter months and a strong dispersion(RMSE≥35.00 mm)in summer months.TRMM showed a relatively low correlation with station observations in winter months(correlation coefficients≤0.70).The capture performance analysis showed that ERA5,GPCC,and TRMM had lower POD and ETS values and higher FAR values in Northwest China as the precipitation intensity increased.ERA5 showed a high capture performance for small precipitation events and a slower decreasing trend of POD as the precipitation intensity increased.GPCC had the lowest FAR values.TRMM was statistically ineffective for predicting the occurrence of daily precipitation events.The findings provide a reference for data users to select appropriate datasets in Northwest China and for data developers to develop new precipitation products in the future.

A Novel Hybrid FA-Based LSSVR Learning Paradigm for Hydropower Consumption Forecasting

Due to the nonlinearity and nonstationary of hydropower market data, a novel hybrid learning paradigm is proposed to predict hydropower consumption, by incorporating firefly algorithm （FA） into least square support vector regression （LSSVR）, i.e., FA-based LSSVR model. In the novel model, the powerful and effective artificial intelligence （AI） technique, i.e., LSSVR, is employed to forecast hydropower consumption. Furthermore, a promising AI optimization tool, i.e., FA, is espe- cially introduced to address the crucial but difficult task of parameters determination in LSSVR （e.g., hyper and kernel function parameters）. With the Chinese hydropower consumption as sample data, the empirical study has statistically confirmed the superiority of the novel FA-based LSSVR model to other benchmark models （including existing popular traditional econometric models, AI models and similar hybrid LSSVRs with other popular parameter searching tools）~ in terms of level and direc- tional accuracy. The empirical results also imply that the hybrid FA-based LSSVR learning paradigm with powerful forecasting tool and parameters optimization method can be employed as an effective forecasting tool for not only hydropower consumption but also other complex data.

Application of time series modeling to a national reference frame realization

This paper presents an option for modern dynamic terrestrial reference system realization in Uzbekistan for user needs. An additive model is explored to predict patterns of time series and investigate means of constructing forecast time series models in the future. The main components(trend, periodical, and irregular) of the KIUB(DORIS) and KIT3, TASH, MADK, and MTAL(GNSS) international stations coordinate time series were investigated. It was shown that seasonal nonlinear trends occurred both in the height(U) component of all stations and the east(E) component of high mountainous stations such as MTAL and MADK. The seasonal periodical portion of the time series determined from the additive model has a complicated pattern for all sites and can be explained as both hydrological signals in the region and improvement of observational quality. Amplitudes of the best-fitting sinusoids in the North component ranged between 1.73 and 8.76 mm; the East component ranged between 0.82 and 11.92 mm; and the Up component ranged between 3.11 and 40.81 mm. Regression analysis of the irregular portion of the height component of the two techniques at the Kitab station using tropospheric parameters(pressure and temperature) was confirmed as only 57% of the stochastic portion of the time series.

Crop Yield Forecasted Model Based on Time Series Techniques

Traditional studies on potential yield mainly referred to attainable yield： the maximum yield which could be reached by a crop in a given environment. The new concept of crop yield under average climate conditions was defined in this paper, which was affected by advancement of science and technology. Based on the new concept of crop yield, the time series techniques relying on past yield data was employed to set up a forecasting model. The model was tested by using average grain yields of Liaoning Province in China from 1949 to 2005. The testing combined dynamic n-choosing and micro tendency rectification, and an average forecasting error was 1.24%. In the trend line of yield change, and then a yield turning point might occur, in which case the inflexion model was used to solve the problem of yield turn point.

Monthly and seasonal streamflow forecasting of large dryland catchments in Brazil

Streamflow forecasting in drylands is challenging.Data are scarce,catchments are highly humanmodified and streamflow exhibits strong nonlinear responses to rainfall.The goal of this study was to evaluate the monthly and seasonal streamflow forecasting in two large catchments in the Jaguaribe River Basin in the Brazilian semi-arid area.We adopted four different lead times:one month ahead for monthly scale and two,three and four months ahead for seasonal scale.The gaps of the historic streamflow series were filled up by using rainfall-runoff modelling.Then,time series model techniques were applied,i.e.,the locally constant,the locally averaged,the k-nearest-neighbours algorithm(k-NN)and the autoregressive(AR)model.The criterion of reliability of the validation results is that the forecast is more skillful than streamflow climatology.Our approach outperformed the streamflow climatology for all monthly streamflows.On average,the former was 25%better than the latter.The seasonal streamflow forecasting(SSF)was also reliable(on average,20%better than the climatology),failing slightly only for the high flow season of one catchment(6%worse than the climatology).Considering an uncertainty envelope(probabilistic forecasting),which was considerably narrower than the data standard deviation,the streamflow forecasting performance increased by about 50%at both scales.The forecast errors were mainly driven by the streamflow intra-seasonality at monthly scale,while they were by the forecast lead time at seasonal scale.The best-fit and worst-fit time series model were the k-NN approach and the AR model,respectively.The rainfall-runoff modelling outputs played an important role in improving streamflow forecasting for one streamgauge that showed 35%of data gaps.The developed data-driven approach is mathematical and computationally very simple,demands few resources to accomplish its operational implementation and is applicable to other dryland watersheds.Our findings may be part of drought forecasting systems and potentially help allocating water months in advance.Moreover,the developed strategy can serve as a baseline for more complex streamflow forecast systems.

A Review of Price Forecasting Problem and Techniques in Deregulated Electricity Markets

In deregulated electricity markets, price forecasting is gaining importance between various market players in the power in order to adjust their bids in the day-ahead electricity markets and maximize their profits. Electricity price is volatile but non random in nature making it possible to identify the patterns based on the historical data and forecast. An accurate price forecasting method is an important factor for the market players as it enables them to decide their bidding strategy to maximize profits. Various models have been developed over a period of time which can be broadly classified into two types of models that are mainly used for Electricity Price forecasting are: 1) Time series models;and 2) Simulation based models;time series models are widely used among the two, for day ahead forecasting. The presented work summarizes the influencing factors that affect the price behavior and various established forecasting models based on time series analysis, such as Linear regression based models, nonlinear heuristics based models and other simulation based models.

On Mixed Model for Improvement in Stock Price Forecasting

Stock market trading is an activity in which investors need fast and accurate information to make effective decisions.But the fact is that forecasting stock prices by using various models has been suffering from low accuracy,slow convergence,and complex parameters.This study aims to employ a mixed model to improve the accuracy of stock price prediction.We present how to use a random walk based on jump-diffusion,to obtain stock predictions with a good-fitting degree by adjusting different parameters.Aimed at getting better parameters and then using the time series model to predict the data,we employed the time series model to smooth the sequence utilizing logarithm and difference,which successfully resulted in drawing the auto-correlation figure and partial the auto-correlation figure.According to the comparative analysis,which focuses on checking the mean absolute error,including root mean square error and R square evaluation index,we have drawn a clear conclusion that our mixed model prediction effect is relatively good.In the context of Chinese stocks,the hybrid random walk model is very suitable for predicting stocks.It can“interpret”the randomness of stocks very well,and it also has an unparalleled prediction effect compared with other models.Based on the time series model’s application in this paper,the abovementioned series is more suitable for predicting trends.

A Hybrid Methodology for Short Term Temperature Forecasting

Developing a reliable weather forecasting model is a complicated task, as it requires heavy IT resources as well as heavy investments beyond the financial capabilities of most countries. In Lebanon, the prediction model used by the civil aviation weather service at Rafic Hariri International Airport in Beirut (BRHIA) is the ARPEGE model, (0.5) developed by the weather service in France. Unfortunately, forecasts provided by ARPEGE have been erroneous and biased by several factors such as the chaotic character of the physical modeling equations of some atmospheric phenomena (advection, convection, etc.) and the nature of the Lebanese topography. In this paper, we proposed the time series method ARIMA (Auto Regressive Integrated Moving Average) to forecast the minimum daily temperature and compared its result with ARPEGE. As a result, ARIMA method shows better mean accuracy (91%) over the numerical model ARPEGE (68%), for the prediction of five days in January 2017. Moreover, back to five months ago, in order to validate the accuracy of the proposed model, a simulation has been applied on the first five days of August 2016. Results have shown that the time series ARIMA method has offered better mean accuracy (98%) over the numerical model ARPEGE (89%) for the prediction of five days of August 2016. This paper discusses a multiprocessing approach applied to ARIMA in order to enhance the efficiency of ARIMA in terms of complexity and resources.

A Dynamic Forecasting System with Applications in Production Logistics

Production logistics involve the co-ordination of ac tivities such as production and materials control (PMC), inventory management, p roduct life cycle management, etc. Those activities demand for an accurate forec asting model. However, the conventional methods of making sell and buy decision based on human forecast or conventional moving average and exponential smoothing methods is no longer be sufficient to meet the future need. Furthermore, the un derlying statistics of the market information change from time to time due to a number of reasons such as change of global economic environment, government poli cies and business risks. This demands for highly adaptive forecasting model which is robust enough to response and adapt well to the fast changes in the dat a characteristics, in other words, the trajectory of the "dynamic characteristic s" of the data. In this paper, an adaptive time-series modelling method was proposed for short -term dynamic forecasting. The method employs an autoregressive (AR) time-seri es model to carry out the forecasting process. A modified least mean square (MLM S) adaptive filter algorithm was established for adjusting the AR model coeffici ents so as to minimise the sum of squared of forecasting errors. A prototype dyn amic forecasting system was built based on the adaptive time-series modelling m ethod. Basically, the dynamic forecasting system can be divided into two phases, i.e. the Learning Phase and the Application Phase. The learning procedures star t with the determination of upper limit of the adaptation gain based on the conv ergence in the mean square criterion. Hence, the optimum ELMS filter parameters are determined using an iteration algorithm which changes each filter parameter i.e. the order, the adaptation gain andthe values initial coefficient vector on e by one inside a predetermined iteration range. The set of parameters which giv es the minimum value for sum of squared errors within the iteration range is sel ected as the optimum set of filter parameters. In the Application Phase, the sys tem is operated under a real-time environment. The sampled data is processed by the optimised ELMS filter and the forecasted data are calculated based on the a daptive time-series model. The error of forecasting is continuously monitored w ithin the predefined tolerance. When the system detects excessive forecasting er ror, a feedback alarm signal was issued for system re-calibration. Experimental results indicated that the convergence rate and sum of squared erro rs during initial adaptation could be significantly improved using the MLMS algorithm. The performance of the system was verified through a series of experi ments conducted on the forecast of materials demand and costing in productio n logistics. Satisfactory results were achieved with the forecast errors confini ng within in most instances. Further applications of the system can be found i n sales demand forecast, inventory management as well as collaborative planning, forecast and replenishment (CPFR) in logistics engineering.