Search results for: Statistical forecasting.

Authors: Petar Sarajcev, Josip Vasilj, Damir Jakus

Abstract:

This paper presents a novel statistical description of the counterpoise effective length due to lightning surges, where the (impulse) effective length had been obtained by means of regressive formulas applied to the transient simulation results. The effective length is described in terms of a statistical distribution function, from which median, mean, variance, and other parameters of interest could be readily obtained. The influence of lightning current amplitude, lightning front duration, and soil resistivity on the effective length has been accounted for, assuming statistical nature of these parameters. A method for determining the optimal counterpoise length, in terms of the statistical impulse effective length, is also presented. It is based on estimating the number of dangerous events associated with lightning strikes. Proposed statistical description and the associated method provide valuable information which could aid the design engineer in optimising physical lengths of counterpoises in different grounding arrangements and soil resistivity situations.

Keywords: Counterpoise, Grounding conductor, Effective length, Lightning, Monte Carlo method, Statistical distribution.

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Authors: Rohit Choudhry, Kumkum Garg

Abstract:

In this paper, we propose a hybrid machine learning system based on Genetic Algorithm (GA) and Support Vector Machines (SVM) for stock market prediction. A variety of indicators from the technical analysis field of study are used as input features. We also make use of the correlation between stock prices of different companies to forecast the price of a stock, making use of technical indicators of highly correlated stocks, not only the stock to be predicted. The genetic algorithm is used to select the set of most informative input features from among all the technical indicators. The results show that the hybrid GA-SVM system outperforms the stand alone SVM system.

Keywords: Genetic Algorithms, Support Vector Machines, Stock Market Forecasting.

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Authors: Defu Zhang, Qingshan Jiang, Xin Li

Abstract:

This paper deals with the application of a well-known neural network technique, multilayer back-propagation (BP) neural network, in financial data mining. A modified neural network forecasting model is presented, and an intelligent mining system is developed. The system can forecast the buying and selling signs according to the prediction of future trends to stock market, and provide decision-making for stock investors. The simulation result of seven years to Shanghai Composite Index shows that the return achieved by this mining system is about three times as large as that achieved by the buy and hold strategy, so it is advantageous to apply neural networks to forecast financial time series, the different investors could benefit from it.

Keywords: Data mining, neural network, stock forecasting.

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Authors: Jihye Jeon

Abstract:

This paper analyzes the conceptual framework of three statistical methods, multiple regression, path analysis, and structural equation models. When establishing research model of the statistical modeling of complex social phenomenon, it is important to know the strengths and limitations of three statistical models. This study explored the character, strength, and limitation of each modeling and suggested some strategies for accurate explaining or predicting the causal relationships among variables. Especially, on the studying of depression or mental health, the common mistakes of research modeling were discussed.

Keywords: Multiple regression, path analysis, structural equation models, statistical modeling, social and psychological phenomenon.

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Authors: M. Tarafdar Haque, A.M. Kashtiban

Abstract:

The electric power industry is currently undergoing an unprecedented reform. One of the most exciting and potentially profitable recent developments is increasing usage of artificial intelligence techniques. The intention of this paper is to give an overview of using neural network (NN) techniques in power systems. According to the growth rate of NNs application in some power system subjects, this paper introduce a brief overview in fault diagnosis, security assessment, load forecasting, economic dispatch and harmonic analyzing. Advantages and disadvantages of using NNs in above mentioned subjects and the main challenges in these fields have been explained, too.

Keywords: Neural network, power system, security assessment, fault diagnosis, load forecasting, economic dispatch, harmonic analyzing.

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Authors: Khalid Ali, Manar Jammal

Abstract:

In order to meet the stringent latency and reliability requirements of the upcoming 5G networks, Open Radio Access Networks (O-RAN) have been proposed. The virtualization of O-RAN has allowed it to be treated as a Network Function Virtualization (NFV) architecture, while its components are considered Virtualized Network Functions (VNFs). Hence, intelligent Machine Learning (ML) based solutions can be utilized to apply different resource management and allocation techniques on O-RAN. However, intelligently allocating resources for O-RAN VNFs can prove challenging due to the dynamicity of traffic in mobile networks. Network providers need to dynamically scale the allocated resources in response to the incoming traffic. Elastically allocating resources can provide a higher level of flexibility in the network in addition to reducing the OPerational EXpenditure (OPEX) and increasing the resources utilization. Most of the existing elastic solutions are reactive in nature, despite the fact that proactive approaches are more agile since they scale instances ahead of time by predicting the incoming traffic. In this work, we propose and evaluate traffic forecasting models based on the ML algorithm. The algorithms aim at predicting future O-RAN traffic by using previous traffic data. Detailed analysis of the traffic data was carried out to validate the quality and applicability of the traffic dataset. Hence, two ML models were proposed and evaluated based on their prediction capabilities.

Keywords: O-RAN, traffic forecasting, NFV, ARIMA, LSTM, elasticity.

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Authors: Takashi Sakai, Shinsaku Kikuta, Jun-ichi Koyama

Abstract:

Using a texture database, a statistical estimation of spring-back was conducted in this study on the basis of statistical analysis. Both spring-back in bending deformation and experimental data related to the crystal orientation show significant dispersion. Therefore, a probabilistic statistical approach was established for the proper quantification of these values. Correlation was examined among the parameters F(x) of spring-back, F(x) of the buildup fraction to three orientations after 92° bending, and F(x) at an as-received part on the basis of the three-parameter Weibull distribution. Consequent spring-back estimation using a texture database yielded excellent estimates compared with experimental values.

Keywords: Bending, Spring-back, Database, Crystallographic Orientation, Texture, SEM-EBSD, Weibull distribution, Statistical analysis.

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Authors: S. Kotsiantis, A. Kostoulas, S. Lykoudis, A. Argiriou, K. Menagias

Abstract:

Estimates of temperature values at a specific time of day, from daytime and daily profiles, are needed for a number of environmental, ecological, agricultural and technical applications, ranging from natural hazards assessments, crop growth forecasting to design of solar energy systems. The scope of this research is to investigate the efficiency of data mining techniques in estimating minimum, maximum and mean temperature values. For this reason, a number of experiments have been conducted with well-known regression algorithms using temperature data from the city of Patras in Greece. The performance of these algorithms has been evaluated using standard statistical indicators, such as Correlation Coefficient, Root Mean Squared Error, etc.

Keywords: regression algorithms, supervised machine learning.

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Authors: G. N. Srinivasan, G. Shobha

Abstract:

This paper presents an overview of the methodologies and algorithms for statistical texture analysis of 2D images. Methods for digital-image texture analysis are reviewed based on available literature and research work either carried out or supervised by the authors.

Keywords: Image Texture, Texture Analysis, Statistical Approaches, Structural approaches, spectral approaches, Morphological approaches, Fractals, Fourier Transforms, Gabor Filters, Wavelet transforms.

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Authors: Ioannis Andrianakis, Vasileios Gkatas, Nikos Eleftheriadis, Alexios Ellinidis, Ermioni Avramidou

Abstract:

The paper discusses the main aspects involved in the development of a supply chain management system using the developed PredictionSCMS software as a basis for the discussion. The discussion is focused on three topics: the first is demand forecasting, where we present the predictive algorithms implemented and discuss related concepts such as the calculation of the safety stock, the effect of out-of-stock days etc. The second topic concerns the design of a supply chain, where the core parameters involved in the process are given, together with a methodology of incorporating these parameters in a meaningful order creation strategy. Finally, the paper discusses some critical events that can happen during the operation of a supply chain management system and how the developed software notifies the end user about their occurrence.

Keywords: Demand forecasting, machine learning, risk management, supply chain design.

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Authors: Ibtihaj Al-Siyabi

Abstract:

The crisis of COVID-19 posed enormous challenges to the statistical providers. While official statistics were disrupted by the pandemic and related containment measures, there was a growing and pressing need for real-time data and statistics to inform decisions. This paper gives an account of the way the pandemic impacted the operations of the National Statistical Offices (NSOs) in general in terms of data collection and methods used, and the main challenges encountered by them based on international surveys. It highlights the performance of the Statistical Centre for the Cooperation Council for the Arab Countries of the Gulf, GCC-STAT, and its responsiveness to the pandemic placing special emphasis on environmental statistics. The paper concludes by confirming the GCC-STAT’s resilience and success in facing the challenges.

Keywords: NSO, COVID-19, pandemic, National Statistical Offices.

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Authors: Theodosia Prodromou

Abstract:

The article investigates how 14- to 15- year-olds build informal conceptions of inferential statistics as they engage in a modelling process and build their own computer simulations with dynamic statistical software. This study proposes four primary phases of informal inferential reasoning for the students in the statistical modeling and simulation process. Findings show shifts in the conceptual structures across the four phases and point to the potential of all of these phases for fostering the development of students- robust knowledge of the logic of inference when using computer based simulations to model and investigate statistical questions.

Keywords: Inferential reasoning, learning, modelling, statistical inference, simulation.

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Authors: S. Kotsiantis, E. Koumanakos, D. Tzelepis, V. Tampakas

Abstract:

This paper explores the effectiveness of machine learning techniques in detecting firms that issue fraudulent financial statements (FFS) and deals with the identification of factors associated to FFS. To this end, a number of experiments have been conducted using representative learning algorithms, which were trained using a data set of 164 fraud and non-fraud Greek firms in the recent period 2001-2002. The decision of which particular method to choose is a complicated problem. A good alternative to choosing only one method is to create a hybrid forecasting system incorporating a number of possible solution methods as components (an ensemble of classifiers). For this purpose, we have implemented a hybrid decision support system that combines the representative algorithms using a stacking variant methodology and achieves better performance than any examined simple and ensemble method. To sum up, this study indicates that the investigation of financial information can be used in the identification of FFS and underline the importance of financial ratios.

Keywords: Machine learning, stacking, classifier.

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Authors: Achela K. Fernando, Xiujuan Zhang, Peter F. Kinley

Abstract:

A feed-forward, back-propagation Artificial Neural Network (ANN) model has been used to forecast the occurrences of wastewater overflows in a combined sewerage reticulation system. This approach was tested to evaluate its applicability as a method alternative to the common practice of developing a complete conceptual, mathematical hydrological-hydraulic model for the sewerage system to enable such forecasts. The ANN approach obviates the need for a-priori understanding and representation of the underlying hydrological hydraulic phenomena in mathematical terms but enables learning the characteristics of a sewer overflow from the historical data. The performance of the standard feed-forward, back-propagation of error algorithm was enhanced by a modified data normalizing technique that enabled the ANN model to extrapolate into the territory that was unseen by the training data. The algorithm and the data normalizing method are presented along with the ANN model output results that indicate a good accuracy in the forecasted sewer overflow rates. However, it was revealed that the accurate forecasting of the overflow rates are heavily dependent on the availability of a real-time flow monitoring at the overflow structure to provide antecedent flow rate data. The ability of the ANN to forecast the overflow rates without the antecedent flow rates (as is the case with traditional conceptual reticulation models) was found to be quite poor.

Keywords: Artificial Neural Networks, Back-propagationlearning, Combined sewer overflows, Forecasting.

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Authors: Salvatore Marra, Francesco C. Morabito

Abstract:

In this paper we present an efficient approach for the prediction of two sunspot-related time series, namely the Yearly Sunspot Number and the IR5 Index, that are commonly used for monitoring solar activity. The method is based on exploiting partially recurrent Elman networks and it can be divided into three main steps: the first one consists in a “de-rectification" of the time series under study in order to obtain a new time series whose appearance, similar to a sum of sinusoids, can be modelled by our neural networks much better than the original dataset. After that, we normalize the derectified data so that they have zero mean and unity standard deviation and, finally, train an Elman network with only one input, a recurrent hidden layer and one output using a back-propagation algorithm with variable learning rate and momentum. The achieved results have shown the efficiency of this approach that, although very simple, can perform better than most of the existing solar activity forecasting methods.

Keywords: Elman neural networks, sunspot, solar activity, time series prediction.

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Authors: Jimeng Shi, Mahek Jain, Giri Narasimhan

Abstract:

Time Series Forecasting (TSF) is used to predict the target variables at a future time point based on the learning from previous time points. To keep the problem tractable, learning methods use data from a fixed length window in the past as an explicit input. In this paper, we study how the performance of predictive models change as a function of different look-back window sizes and different amounts of time to predict into the future. We also consider the performance of the recent attention-based transformer models, which had good success in the image processing and natural language processing domains. In all, we compare four different deep learning methods (Recurrent Neural Network (RNN), Long Short-term Memory (LSTM), Gated Recurrent Units (GRU), and Transformer) along with a baseline method. The dataset (hourly) we used is the Beijing Air Quality Dataset from the website of University of California, Irvine (UCI), which includes a multivariate time series of many factors measured on an hourly basis for a period of 5 years (2010-14). For each model, we also report on the relationship between the performance and the look-back window sizes and the number of predicted time points into the future. Our experiments suggest that Transformer models have the best performance with the lowest Mean   Absolute Errors (MAE = 14.599, 23.273) and Root Mean Square Errors (RSME = 23.573, 38.131) for most of our single-step and multi-steps predictions. The best size for the look-back window to predict 1 hour into the future appears to be one day, while 2 or 4 days perform the best to predict 3 hours into the future.

Keywords: Air quality prediction, deep learning algorithms, time series forecasting, look-back window.

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Authors: Darren Zou

Abstract:

Forecasting the stock market is a very challenging task. Various economic indicators such as GDP, exchange rates, interest rates, and unemployment have a substantial impact on the stock market. Time series models are the traditional methods used to predict stock market changes. In this paper, a machine learning method, Bayesian Additive Regression Tree (BART) is used in predicting stock market indexes based on multiple economic indicators. BART can be used to model heterogeneous treatment effects, and thereby works well when models are misspecified. It also has the capability to handle non-linear main effects and multi-way interactions without much input from financial analysts. In this research, BART is proposed to provide a reliable prediction on day-to-day stock market activities. By comparing the analysis results from BART and with time series method, BART can perform well and has better prediction capability than the traditional methods.

Keywords: Bayesian, Forecast, Stock, BART.

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Authors: A. Maghari, V. H. Maleki

Abstract:

In this paper, we present a quantum statistical mechanical formulation from our recently analytical expressions for partial-wave transition matrix of a three-particle system. We report the quantum reactive cross sections for three-body scattering processes 1+(2,3)→1+(2,3) as well as recombination 1+(2,3)→1+(3,1) between one atom and a weakly-bound dimer. The analytical expressions of three-particle transition matrices and their corresponding cross-sections were obtained from the threedimensional Faddeev equations subjected to the rank-two non-local separable potentials of the generalized Yamaguchi form. The equilibrium quantum statistical mechanical properties such partition function and equation of state as well as non-equilibrium quantum statistical properties such as transport cross-sections and their corresponding transport collision integrals were formulated analytically. This leads to obtain the transport properties, such as viscosity and diffusion coefficient of a moderate dense gas.

Keywords: Statistical mechanics, Nonlocal separable potential, three-body interaction, Faddeev equations.

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Authors: Ehsan Bashiri

Abstract:

A 7-step method (with 25 sub-steps) to assess risk of air pollutants is introduced. These steps are: pre-considerations, sampling, statistical analysis, exposure matrix and likelihood, doseresponse matrix and likelihood, total risk evaluation, and discussion of findings. All mentioned words and expressions are wellunderstood; however, almost all steps have been modified, improved, and coupled in such a way that a comprehensive method has been prepared. Accordingly, the SADRA (Statistical Analysis-Driven Risk Assessment) emphasizes extensive and ongoing application of analytical statistics in traditional risk assessment models. A Sulfur Dioxide case study validates the claim and provides a good illustration for this method.

Keywords: Criteria air pollutants, Matrix of risk, Riskassessment, Statistical analysis.

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Authors: Yunus Doğan, Ahmet Durap

Abstract:

Coastal regions are the one of the most commonly used places by the natural balance and the growing population. In coastal engineering, the most valuable data is wave behaviors. The amount of this data becomes very big because of observations that take place for periods of hours, days and months. In this study, some statistical methods such as the wave spectrum analysis methods and the standard statistical methods have been used. The goal of this study is the discovery profiles of the different coast areas by using these statistical methods, and thus, obtaining an instance based data set from the big data to analysis by using data mining algorithms. In the experimental studies, the six sample data sets about the wave behaviors obtained by 20 minutes of observations from Mersin Bay in Turkey and converted to an instance based form, while different clustering techniques in data mining algorithms were used to discover similar coastal places. Moreover, this study discusses that this summarization approach can be used in other branches collecting big data such as medicine.

Keywords: Clustering algorithms, coastal engineering, data mining, data summarization, statistical methods.

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Authors: C. Temaneh Nyah

Abstract:

The analysis of electromagnetic environment using deterministic mathematical models is characterized by the impossibility of analyzing a large number of interacting network stations with a priori unknown parameters, and this is characteristic, for example, of mobile wireless communication networks. One of the tasks of the tools used in designing, planning and optimization of mobile wireless network is to carry out simulation of electromagnetic environment based on mathematical modelling methods, including computer experiment, and to estimate its effect on radio communication devices. This paper proposes the development of a statistical model of electromagnetic environment of a mobile wireless communication network by describing the parameters and factors affecting it including the propagation channel and their statistical models.

Keywords: Electromagnetic Environment, Statistical model, Wireless communication network.

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Authors: Yoshio Kurosawa

Abstract:

The applications of soundproof materials for reduction of high frequency automobile interior noise have been researched. This paper presents a sound pressure prediction technique including wind noise by Hybrid Statistical Energy Analysis (HSEA) in order to reduce weight of acoustic insulations. HSEA uses both analytical SEA and experimental SEA. As a result of chassis dynamo test and road test, the validity of SEA modeling was shown, and utility of the method was confirmed.

Keywords: Vibration, noise, car, statistical energy analysis.

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Authors: Karim Hamidi Machekposhti, Hossein Sedghi, Abdolrasoul Telvari, Hossein Babazadeh

Abstract:

Rainfall and runoff phenomenon is a chaotic and complex outcome of nature which requires sophisticated modelling and simulation methods for explanation and use. Time Series modelling allows runoff data analysis and can be used as forecasting tool. In the paper attempt is made to model river runoff data and predict the future behavioural pattern of river based on annual past observations of annual river runoff. The river runoff analysis and predict are done using ARIMA model. For evaluating the efficiency of prediction to hydrological events such as rainfall, runoff and etc., we use the statistical formulae applicable. The good agreement between predicted and observation river runoff coefficient of determination (R²) display that the ARIMA (4,1,1) is the suitable model for predicting Karkheh River runoff at Iran.

Keywords: Time series modelling, ARIMA model, River runoff, Karkheh River, CLS method.

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Authors: Khalid Elasnaoui, Brahim Aksasse, Mohammed Ouanan

Abstract:

In this paper, we are interested in the problem of finding similar images in a large database. For this purpose we propose a new algorithm based on a combination of the 2-D histogram intersection in the HSV space and statistical moments. The proposed histogram is based on a 3x3 window and not only on the intensity of the pixel. This approach overcome the drawback of the conventional 1-D histogram which is ignoring the spatial distribution of pixels in the image, while the statistical moments are used to escape the effects of the discretisation of the color space which is intrinsic to the use of histograms. We compare the performance of our new algorithm to various methods of the state of the art and we show that it has several advantages. It is fast, consumes little memory and requires no learning. To validate our results, we apply this algorithm to search for similar images in different image databases.

Keywords: 2-D histogram, Statistical moments, Indexing, Similarity distance, Histograms intersection.

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Authors: Ε. Giovanis

Abstract:

In this paper we present an autoregressive model with neural networks modeling and standard error backpropagation algorithm training optimization in order to predict the gross domestic product (GDP) growth rate of four countries. Specifically we propose a kind of weighted regression, which can be used for econometric purposes, where the initial inputs are multiplied by the neural networks final optimum weights from input-hidden layer after the training process. The forecasts are compared with those of the ordinary autoregressive model and we conclude that the proposed regression-s forecasting results outperform significant those of autoregressive model in the out-of-sample period. The idea behind this approach is to propose a parametric regression with weighted variables in order to test for the statistical significance and the magnitude of the estimated autoregressive coefficients and simultaneously to estimate the forecasts.

Keywords: Autoregressive model, Error back-propagation Feed-Forward neural networks, , Gross Domestic Product

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Authors: Seyed Hossein Iranmanesh, Mansoureh Zarezadeh

Abstract:

This paper presents an application of Artificial Neural Network (ANN) to forecast actual cost of a project based on the earned value management system (EVMS). For this purpose, some projects randomly selected based on the standard data set , and it is produced necessary progress data such as actual cost ,actual percent complete , baseline cost and percent complete for five periods of project. Then an ANN with five inputs and five outputs and one hidden layer is trained to produce forecasted actual costs. The comparison between real and forecasted data show better performance based on the Mean Absolute Percentage Error (MAPE) criterion. This approach could be applicable to better forecasting the project cost and result in decreasing the risk of project cost overrun, and therefore it is beneficial for planning preventive actions.

Keywords: Earned Value Management System (EVMS), Artificial Neural Network (ANN), Estimate At Completion, Forecasting Methods, Project Performance Measurement.

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Authors: Nang Thwe Thwe Oo

Abstract:

Traditional object segmentation methods are time consuming and computationally difficult. In this paper, onedimensional object detection along the secant lines is applied. Statistical features of texture images are computed for the recognition process. Example matrices of these features and formulae for calculation of similarities between two feature patterns are expressed. And experiments are also carried out using these features.

Keywords: 1-D object segmentation, secant lines, objectoccurrence(frequency) matrix, contiguity matrix, statistical features.

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Authors: Juliana Barcelos Cordeiro, Khashayar Mahani, Farbod Farzan, Mohsen A. Jafari

Abstract:

Energy disaggregation has been focused by many energy companies since energy efficiency can be achieved when the breakdown of energy consumption is known. Companies have been investing in technologies to come up with software and/or hardware solutions that can provide this type of information to the consumer. On the other hand, not all people can afford to have these technologies. Therefore, in this paper, we present a methodology for breaking down the aggregate consumption and identifying the highdemanding end-uses profiles. These energy profiles will be used to build the forecast model for optimal control purpose. A facility with high cooling load is used as an illustrative case study to demonstrate the results of proposed methodology. We apply a high level energy disaggregation through a pattern recognition approach in order to extract the consumption profile of its rooftop packaged units (RTUs) and present a forecast model for the energy consumption.  

Keywords: Energy consumption forecasting, energy efficiency, load disaggregation, pattern recognition approach.

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Authors: Satyendra Nath Mandal, J. Pal Choudhury, Dilip De, S. R. Bhadra Chaudhuri

Abstract:

The production of a plant can be measured in terms of seeds. The generation of seeds plays a critical role in our social and daily life. The fruit production which generates seeds, depends on the various parameters of the plant, such as shoot length, leaf number, root length, root number, etc When the plant is growing, some leaves may be lost and some new leaves may appear. It is very difficult to use the number of leaves of the tree to calculate the growth of the plant.. It is also cumbersome to measure the number of roots and length of growth of root in several time instances continuously after certain initial period of time, because roots grow deeper and deeper under ground in course of time. On the contrary, the shoot length of the tree grows in course of time which can be measured in different time instances. So the growth of the plant can be measured using the data of shoot length which are measured at different time instances after plantation. The environmental parameters like temperature, rain fall, humidity and pollution are also play some role in production of yield. The soil, crop and distance management are taken care to produce maximum amount of yields of plant. The data of the growth of shoot length of some mustard plant at the initial stage (7,14,21 & 28 days after plantation) is available from the statistical survey by a group of scientists under the supervision of Prof. Dilip De. In this paper, initial shoot length of Ken( one type of mustard plant) has been used as an initial data. The statistical models, the methods of fuzzy logic and neural network have been tested on this mustard plant and based on error analysis (calculation of average error) that model with minimum error has been selected and can be used for the assessment of shoot length at maturity. Finally, all these methods have been tested with other type of mustard plants and the particular soft computing model with the minimum error of all types has been selected for calculating the predicted data of growth of shoot length. The shoot length at the stage of maturity of all types of mustard plants has been calculated using the statistical method on the predicted data of shoot length.

Keywords: Fuzzy time series, neural network, forecasting error, average error.

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Authors: Souhir Ben Amor, Heni Boubaker, Lotfi Belkacem

Abstract:

This aims of this paper is to forecast the electricity spot prices. First, we focus on modeling the conditional mean of the series so we adopt a generalized fractional -factor Gegenbauer process (k-factor GARMA). Secondly, the residual from the -factor GARMA model has used as a proxy for the conditional variance; these residuals were predicted using two different approaches. In the first approach, a local linear wavelet neural network model (LLWNN) has developed to predict the conditional variance using the Back Propagation learning algorithms. In the second approach, the Gegenbauer generalized autoregressive conditional heteroscedasticity process (G-GARCH) has adopted, and the parameters of the k-factor GARMA-G-GARCH model has estimated using the wavelet methodology based on the discrete wavelet packet transform (DWPT) approach. The empirical results have shown that the k-factor GARMA-G-GARCH model outperform the hybrid k-factor GARMA-LLWNN model, and find it is more appropriate for forecasts.

Keywords: k-factor, GARMA, LLWNN, G-GARCH, electricity price, forecasting.

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