Nonlinear Time Series Forecasting Research Articles

GARCH Models and Distributions Comparison for Nonlinear Time Series with Volatilities

The Generalized Autoregressive Conditional Heteroskedasticity (GARCH) model is extensively used for handling volatilities. However, with numerous extensions to the standard GARCH model, selecting the most suitable model for forecasting price volatilities becomes challenging. This study aims to examine the performance of different GARCH models in forecasting crude oil price volatilities using West Texas Intermediate (WTI) data. The models considered are the standard GARCH, Integrated GARCH (IGARCH), Exponential GARCH (EGARCH), and Golsten, Jagannathan, and Runkle GARCH (GJR-GARCH), each with normal distribution, Student’s t-distribution, and Generalized Error Distribution (GED). To evaluate the performance of each model, the Akaike Information Criteria (AIC) and Bayesian Information Criteria (BIC) are used as the model selection criteria, along with forecast accuracy measures such as absolute error, root mean squared error (RMSE), and mean absolute error (MAE). Post-estimation tests, including the Autoregressive Conditional Heteroskedasticity Lagrange Multiplier (ARCH-LM) test and the Ljung-Box test, are conducted to ensure the adequacy of all models. The results reveal that all GARCH models are suitable for modeling the data, as indicated by statistically significant estimated parameters and satisfactory post-estimation outcomes. However, the EGARCH (1, 1) model, particularly with Student’s t-distribution, outperforms other models in both data fitting and accurate forecasting of nonlinear time series.

Depth asynchronous time delay reservoir for nonlinear time series forecasting task

The forecasting of nonlinear time series has a wide range of applications both in theoretical research and industrial production, as the fitting of nonlinear systems, the early warning of sunspot activity and the prediction of network traffic peaks in advance. These tasks require models with strong nonlinear mapping capabilities and sufficient short-term memory capacity. Single-node time delay Reservoir (TDR) have been frequently applied on nonlinear time series forecasting tasks. To address the lack of memory capacity of traditional TDR and its extended version (Delay Decoupled Reservoir (DDR), Deep Time-Delay Reservoir (DTDR)), we propose a Depth Asynchronous Time-Delay Reservoir (DATDR) model. Firstly, the model retains the deep network structure of the DTDR to ensure the dynamic properties of the model, and the history states of each layer are from the previous layers instead of the current layer. Secondly, the same signal input method as the DDR is used, i.e., each layer is fed with the original signal, and this data input method ensures that the feature of signal does not decay gradually during the transmission between layers. Finally, a time delay operator is inserted into two adjacent layers, and the memory capacity of the model could be controlled effectively by adjusting the delay time of the time delay operator to accommodate some time series prediction tasks that require long memory capacity. In this paper, eight datasets from three different types are used to validate the proposed model, including NARMA10-30, Mackey-Glass Chaos time series, He ́non map series, Sunspot Sequence, and two real network traffic datasets. Experiments show that proposed model gets significant improvement in memory capacity compared with TDR, DDR, and DTDR, and performs better for some nonlinear time series datasets especially some long-term memory datasets.

FUZZY MODEL FOR TIME SERIES FORECASTING

Abstract: In 2007, in Kazakhstan, there was a transition of TDM (Time Division Multiplexing) circuit-switched technologies to IP (Internet Protocol) packet technology, which created a modern infrastructure for the ICT (information communication technologies) sphere. The advent of the IoT (Internet of Things) concept has led to the growth of a functioning network at a faster rate. It is currently developing in the direction of a cognitive infocommunication network. Its evolutionary development is characterized by a change in the volume of transmitted information, types of its presentation, methods of transmission and storage, the number of sources and consumers, distribution among users, requirements for timeliness and reliability (quality) [1]. Types of traffic and their structure are changing, therefore data processing becomes more complicated. For this reason, the tasks of analyzing and predicting network traffic remain relevant.
 In this work, the prediction of the measured traffic on a real network is performed. The series under study shows the totality of packets transmitted over the backbone network for each second. Forecasting of a one-dimensional time series is carried out on the basis of fuzzy logic methods. This class of models is well suited for modeling nonlinear systems and time series forecasting. The use of fuzzy sets is based on the ability of fuzzy models to approximate functions, as well as on the readability of rules using linguistic variables. The results of the software algorithm of fuzzy inference models were obtained using the Python environment. Membership functions, predictive graphs were built and their evaluation was carried out. The numerical values of the root mean square error (MSE) are calculated. As a result, it was found that the Cheng fuzzy prediction model has higher forecast accuracy than the Chen forecasting method.

Serial-parallel dynamic echo state network: A hybrid dynamic model based on a chaotic coyote optimization algorithm for wind speed prediction

Multiple reservoirs have been widely used in nonlinear time series forecasting. The hybrid approach is recognized as the mainstream forecasting method in complex wind speed prediction systems. However, application research and error correction of the multiple reservoirs hybrid model in the wind energy domain are still insufficient. Therefore, a serial-parallel dynamic echo state network (SP-ESN) with dual dynamic characteristics is proposed firstly. Its serial structure can capture the short-term memory information of the sequence and dynamically select the length of the training set, while the parallel structure has the ability to automatically correct the prediction error of the serial structure. Then, a dynamic prediction model based on phase space reconstruction that includes the improved complete ensemble empirical mode decomposition with adaptive noise (ICEEMDAN) method, the SP-ESN and the chaotic coyote optimization algorithm (CCOA) is designed in this paper. After data preprocessing of the original sequence by ICEEMDAN, the generated decomposed subsequence is input into the SP-ESN model for prediction and the final forecasting value is obtained accordingly. The CCOA is used to optimize the developed SP-ESN model parameters. Five wind speed datasets from Ningxia Hui Autonomous Region and Qinghai Province of China are selected for experiments. Six point prediction evaluation metric, forecasting efficiency and Diebold-Mariano test are used to evaluate the performance of the proposed model in ultra-short term wind speed forecasting. The case study results show that the proposed hybrid model achieves satisfactory performance compared with 5 datasets and 14 models, with mean absolute percentage error (MAPE) of 0.8405%, 1.2207%, 0.5163% 0.9791% and 0.3826%, respectively.

Piecewise forecasting of nonlinear time series with model tree dynamic Bayesian networks

Piecewise forecasting of nonlinear time series with model tree dynamic Bayesian networks

Chaos based portfolio selection: A nonlinear dynamics approach

Time series forecasting is of fundamental importance for financial market prediction and, consequently, for portfolio allocation strategies. However, non-stationarity and non-linearity of most financial time series often make these tasks difficult to perform. In this paper, we propose a methodology based on chaos and dynamical systems theory for non-linear time series forecasting and investment strategy development, which is able to correctly make predictions at long time horizons. We construct Constant Chaoticity Portfolios (CCP) and evaluate their performances on the survival components of the STOXX Europe 50 index and the Hang-Seng index. Results show that the CCP overwhelms several competing alternatives, both in terms of net profits and risk-return profiles. Our findings are confirmed by a sensitivity analysis on the parameters of the underlying model and over different choices of forecast horizons.

Analysis of modified time series prediction techniques: A case study with bakery industry

In the current scenario, it is a very difficult task to predict the demand for a particular product in the market. It is very challenging work for the industries to manufacture the product without being acquainted with the actual sale. To meet the demand of customers and to make the supply chain process optimize various strategies are being adopted at each node of the supply chain. Manufacturing the product by the market consumption significantly affects the revenue generation of small and medium scale enterprises especially of the FMCG industry.In this paper, a case study of a medium-scale industry named “Gopal Ji Food Products.” Kosi Kalan (U.P.) has been performed, Highlights of this case study have been kept to know the demand for the number of boxes of biscuits which are to be distributed in the market. The primary work is done by collecting historical data of the requirement of boxes for the last 104 weeks (April 2017 to March 2018). With the help of this data, the demand pattern is known. After knowing the demand pattern, an attempt has been made to develop a prediction model using time series forecasting to acquaint with the number of boxes to be manufactured in advance. The result shows that the data obtained through Non-linear Autoregressive time series forecasting can be used for better planning and fulfilling market demand on time and making the whole supply chain more optimize, effective, and cost-efficient.

Multiscaled Neural Autoregressive Distributed Lag: A New Empirical Mode Decomposition Model for Nonlinear Time Series Forecasting.

Forecasting has always been the cornerstone of machine learning and statistics. Despite the great evolution of the time series theory, forecasters are still in the hunt for better models to make more accurate decisions. The huge advances in neural networks over the last years has led to the emergence of a new generation of effective models replacing classic econometric models. It is in this direction that we propose, in this paper, a new multiscaled Feedforward Neural Network (FNN), with the aim of forecasting multivariate time series. This new model, called Empirical Mode Decomposition (EMD)-based Neural ARDL, is inspired from the well-known Autoregressive Distributed Lag (ARDL) model being our proposal founded upon the concepts of nonlinearity, EMD-multiresolution and neural networks. These features give the model the ability to effectively capture many nonlinear patterns like the ones often present in econophysical time series, such as nonlinear trends, seasonal effects, long-range dependency, etc. The proposed algorithm can be summarized into the following four basic tasks: (i) EMD breaking-down multivariate time series into different resolution levels, (ii) feeding EMD components from the same levels into a number of feedforward neural ARDL models, (iii) from one level to the next, extrapolating the component corresponding to the response variable (scalar output) a number of steps ahead, and finally, (iv) recombining level-by-level forecasts into a single output. An optimal learning scheme is rigorously designed for efficiently training the new proposed architecture. The approach is finally tested and compared to a number of powerful benchmark models, where experiments are conducted on real-world data.

Stock index prediction based on wavelet transform and FCD‐MLGRU

AbstractWith the development of artificial intelligence, deep learning is widely used in the field of nonlinear time series forecasting. It is proved in practice that deep learning models have higher forecasting accuracy compared with traditional linear econometric models and machine learning models. With the purpose of further improving forecasting accuracy of financial time series, we propose the WT‐FCD‐MLGRU model, which is the combination of wavelet transform, filter cycle decomposition and multilag neural networks. Four major stock indices are chosen to test the forecasting performance among traditional econometric model, machine learning model and deep learning models. According to the result of empirical analysis, deep learning models perform better than traditional econometric model such as autoregressive integrated moving average and improved machine learning model SVR. Besides, our proposed model has the minimum forecasting error in stock index prediction.

Stock price forecast based on combined model of ARI-MA-LS-SVM

Stock forecasting is a very complex non-stationary, nonlinear time series forecasting, and is often affected by many factors, making it difficult to predict it with a simple model. Support vector machine (SVM) is one of the common data mining methods in the field of machine learning. It has outstanding advantages compared with other methods and it is widely used in various fields. However, there are still many problems in the practical application of the method, and the model itself has many fields that need to be improved. The purpose of this paper is to accurately predict the trend of stock prices, providing a reference model for the trend of stock market and the tracking method of stock price prediction, and provide value reference for research on the forecasting model of stock market and investor’s investment decision. Research using a combined model to predict stock market trends whether will have a significant improvement compared to using a single model to forecast that. The method of this paper is to analyze the shortcomings of current stock market forecasting methods and standard support vector machines firstly, at the same time, based on this, a cumulative auto-regressive moving average is proposed, which combines the least squares support vector machine synthesis model (ARI-MA-LS-SVM) to make basic predictions for the stock market. Secondly, process the data first for the predictive indicators by using cumulative auto-regressive moving average. Then, use the least squares support vector machine of simple indicator system to predict stock price fluctuations. Therefore, it can be concluded that the combined model based on ARI-MA-LS-SVM is more suitable for stock price forecasting than the single forecasting model, and the actual performance is better. At the same time, a large number of simulation experiments show that the algorithm of multiple model’s fusion can achieve the expected effect, which indicate that the model has universal applicability, market applicability and stability feasibility. This model can bring some guidance and reference value for many investors and market regulators.

A new Neuro-Fuzzy Inference System with Dynamic Neurons (NFIS-DN) for system identification and time series forecasting

A new Neuro-Fuzzy Inference System with Dynamic Neurons or NFIS-DN is presented here for discrete time dynamic system identification and time series forecasting problems. The proposed dynamic system based neuron, referred to as Dynamic Neuron (DN) is realized by a discrete-time nonlinear state-space model. The DN is designed such way, that the output considers only the effect of finite past instances, enabling the system with finite memory. The NFIS-DN model has five layers, and DNs are employed only in the layers handling crisp values. The antecedent and the consequent parameters of NFIS-DN are updated using a self-regulated backpropagation through time learning algorithm. The performance evaluation of NFIS-DN has been carried-out using benchmark problems in the areas of nonlinear system identification and time series forecasting. The results are compared with the state-of-the-art method on the neural fuzzy networks. The obtained results clearly suggest that the NFIS-DN performs significantly better while using a smaller or similar number of fuzzy rules. Finally the practical application of the NFIS-DN has been demonstrated using two real-world problems.

Several Aspects of Nonparametric Prediction of Nonlinear Time Series

Nonparametric regression is an alternative to the parametric approach, which consists of applying parametric models, i.e. models of the certain functional form with a fixed number of parameters. As opposed to the parametric approach, nonparametric models have a general form, which can be approximated increasingly precisely when the sample size grows. Hereby they do not impose such restricted assumptions about the form of the modelling dependencies and in consequence, they are more flexible and let the data speak for themselves. That is why they are a promising tool for forecasting, especially in case of nonlinear time series. One of the most popular nonparametric regression method is the Nadaraya- Watson kernel smoothing. Nowadays, there are a number of variations of this method, like the local-linear kernel estimator, which combines the local linear approximation and the kernel estimator. In the paper a Monte Carlo study is conducted in order to assess the usefulness of the kernel smoothers to nonlinear time series forecasting and to compare them with the other techniques of forecasting.

Improving forecasting accuracy for stock market data using EMD-HW bagging.

Many researchers documented that the stock market data are nonstationary and nonlinear time series data. In this study, we use EMD-HW bagging method for nonstationary and nonlinear time series forecasting. The EMD-HW bagging method is based on the empirical mode decomposition (EMD), the moving block bootstrap and the Holt-Winter. The stock market time series of six countries are used to compare EMD-HW bagging method. This comparison is based on five forecasting error measurements. The comparison shows that the forecasting results of EMD-HW bagging are more accurate than the forecasting results of the fourteen selected methods.

Foreign exchange rates forecasting with an EMD-LSTM neural networks model

Since financial time series are inherently noisy and unstable, it is quite challenging to enhance the forecasting accuracy. To alleviate the adverse effect, in this study, the combined model of Empirical Mode Decomposition (EMD) and Long Short-Term Memory (LSTM) is proposed. In this model with the EMD, the original time series are decomposed into IMF sequence and residual sequence. LSTM is applied to the financial forecasting model. The proposed model present superior forecasting capacity, which proves that machine learning performs better in nonlinear time series forecasting.

Short-Time Traffic State Forecasting Using Adaptive Neighborhood Selection Based on Expansion Strategy

Short-term traffic state forecasting is critical for real-time traffic control, but due to its complexity and its nonlinear nature, it is difficult to obtain a high degree of precision. The “k-nearest neighbors” model has been widely used to solve nonlinear regression and time series forecasting. This paper presents a traffic state forecasting method using adaptive neighborhood selection based on expansion strategy to search manifold neighbors to get higher precision with manifold neighbors. We propose a method of linear structure to handle the traffic data in Euclidean space to find a manifold neighbor that is more suitable for predicting traffic states. The results of extensive comparison experiments indicate that the proposed model can produce more accurate forecasting results than other classic algorithms.

Design of Experiment to Optimize the Architecture of Deep Learning for Nonlinear Time Series Forecasting

The neural architecture is very substantial in order to construct a neural network model that produce a minimum error. Several factors among others include the input choice, the number of hidden layers, the series length, and the activation function. In this paper we present a design of experiment in order to optimize the neural network model. We conduct a simulation study by modeling the data generated from a nonlinear time series model, called subset 3 exponential smoothing transition auto-regressive (ESTAR ([3]). We explore a deep learning model, called deep feedforward network and we compare it to the single hidden layer feedforward neural network. Our experiment resulted in that the input choice is the most important factor in order to improve the forecast performance as well as the deep learning model is the promising approach for forecasting task.

An ARMA Type Pi-Sigma Artificial Neural Network for Nonlinear Time Series Forecasting

Abstract Real-life time series have complex and non-linear structures. Artificial Neural Networks have been frequently used in the literature to analyze non-linear time series. High order artificial neural networks, in view of other artificial neural network types, are more adaptable to the data because of their expandable model order. In this paper, a new recurrent architecture for Pi-Sigma artificial neural networks is proposed. A learning algorithm based on particle swarm optimization is also used as a tool for the training of the proposed neural network. The proposed new high order artificial neural network is applied to three real life time series data and also a simulation study is performed for Istanbul Stock Exchange data set.

WITHDRAWN: Forecasting of nonlinear time series using artificial neural network

Abstract When forecasting time series, it is important to classify them according to linearity behavior; the linear time series remains at the forefront of academic and applied research. It has often been found that simple linear time series models usually leave certain aspects of economic and financial data unexplained. The dynamic behavior of most of the time series in our real life, with its autoregressive and inherited moving average terms, pose the challenge to forecast nonlinear times series that contain inherited moving average terms using computational intelligence methodologies such as neural networks. It is rare to find studies that concentrate on forecasting nonlinear times series that contain moving average terms. In this study, we demonstrate that the common neural networks are not efficient for recognizing the behavior of nonlinear or dynamic time series which has moving average terms and hence low forecasting capability. This leads to the importance of formulating new models of neural networks such as Deep Learning neural networks with or without hybrid methodologies such as Fuzzy Logic.

Adaptive Forecasting of Non-Stationary Nonlinear Time Series Based on the Evolving Weighted Neuro-Neo-Fuzzy-ANARX-Model

An evolving weighted neuro-neo-fuzzy- ANARX model and its learn ing procedures are introduced in the article. This system is basically used for time series forecasting. It's based on neo-fuzzy elements. This system may be considered as a pool of elements that process data in a parallel manner. The proposed evolving system may provide online processing data streams.

A Multi Time Scale Wind Power Forecasting Model of a Chaotic Echo State Network Based on a Hybrid Algorithm of Particle Swarm Optimization and Tabu Search

The uncertainty and regularity of wind power generation are caused by wind resources’ intermittent and randomness. Such volatility brings severe challenges to the wind power grid. The requirements for ultrashort-term and short-term wind power forecasting with high prediction accuracy of the model used, have great significance for reducing the phenomenon of abandoned wind power , optimizing the conventional power generation plan, adjusting the maintenance schedule and developing real-time monitoring systems. Therefore, accurate forecasting of wind power generation is important in electric load forecasting. The echo state network (ESN) is a new recurrent neural network composed of input, hidden layer and output layers. It can approximate well the nonlinear system and achieves great results in nonlinear chaotic time series forecasting. Besides, the ESN is simpler and less computationally demanding than the traditional neural network training, which provides more accurate training results. Aiming at addressing the disadvantages of standard ESN, this paper has made some improvements. Combined with the complementary advantages of particle swarm optimization and tabu search, the generalization of ESN is improved. To verify the validity and applicability of this method, case studies of multitime scale forecasting of wind power output are carried out to reconstruct the chaotic time series of the actual wind power generation data in a certain region to predict wind power generation. Meanwhile, the influence of seasonal factors on wind power is taken into consideration. Compared with the classical ESN and the conventional Back Propagation (BP) neural network, the results verify the superiority of the proposed method.