Nonlinear Time Series Research Articles

Machine Learning based IoT Flood Rediction Using Data Modeling and Decision Support System

An essential step in supplying data for climate impact studies and evaluations of hydrological processes is rainfall prediction. However, rainfall events are complex phenomenon’s that continue to be difficult to forecast. In this paper , we present unique hybrid models for the prediction of monthly precipitation that include Seasonal Artificial Neural Networks and Discrete wavelet transforms are two pre-processing methods, together with Artificial Neural Networks have two feed forward neural networks. The temporal series of observed monthly rainfall from Vietnam’s Ca Mau hydrological station were decomposed into three subsets by seasonal decomposition and five sub signals and four levels by wavelet analysis. The methods for predicting rainfall that use feed forward artificial neural networks (ANN) and seasonal artificial neural network (SANN) were fed with the processed data. The classic genetic method and simulated annealing method backed by using an integrated moving average and autoregressive moving was contrasted with the predicted models for model evaluation. The results showed that non-stationary regarding issues with non-linear time series, such forecasting rainfall could be satisfactorily simulated. The SANN model was integrated with the wavelet transform and seasonal decomposition are both used. Techniques, however the wavelet transform method produced the most accurate monthly rainfall data, Predictions. Due to the effects of climate change, nations including the Japan, China, the United States of America, and Taiwan, etc., have recently experienced severe and devastating natural disasters. One of the biggest causes of the destruction in Asian nations like china, India, Bangladesh, Sri Lanka, etc. is the flood. The danger of fatality from these floods is increased by 78% as information technology advances; there is a demand for simple access to massive amounts of cloud storage and computing capacity.

Modelling of noise due to impulsive excitation using nonlinear time series analysis

Early acoustic machine design phases should target safety and comfort requirements, minimising the risk of hearing damage and noise exposure and ensuring a pleasant machine sound. Therefore, physical mechanisms of sound generation, propagation and radiation need to be modelled. Today, nonlinear physical relations in vibroacoustic models such as contact problems are mostly linearised. The aim of this paper is to increase the prediction quality of vibroacoustic models so that physical mechanisms behind sound generation due to complex physical, nonlinear phenomena can be better understood. The focus is on sound generation due to impulsive excitation, which is a significant sound generation mechanism in machinery, e.g. considering gears, forming processes (e.g. punching), or road loads of vehicles. We describe a model setup to simulate impulsive excitation on a laboratory scale, where structural vibrations can be analysed. Physical correlations including nonlinear correlations could be identified using nonlinear time series analysis. Recurrence plots will be used to identify features such as phase space contraction, e.g. to identify damping. These features form the basis to deepen the physical understanding of machinery noise, to contribute to enhanced acoustic machine designs and to enhance data-driven modelling using sparse regression in future research.

Directed recurrence networks.

Complex network approaches have attracted a growing interest in the analysis of nonlinear time series. Among other reconstruction methods, it has been shown that the recurrence plot can be used as the adjacency matrix for recurrence networks, expanding the applications of the already successful recurrence analysis. We study here the potential benefits of a directed formulation of recurrence networks through a simple modification of the recurrence plot. As it is directly related to the recurrence analysis field, this approach takes advantage of the progresses regarding the creation and treatment of the recurrence plot. It appears that directed recurrence networks provide more robust results than their undirected counterpart for transitions detection as well as temporal patterns discovery and clustering. New applications for network cleaning and data modeling are also demonstrated.

Spiral bevel gears: Bifurcation and chaos analyses of pure torsional system

The goal of this paper is to provide a detailed analysis of the complex dynamic scenario of spiral bevel gears by considering the torsional shaft stiffness. The dynamic model takes into account: time-dependent stiffness and non-smooth nonlinearity due to the backlash, i.e., teeth contact loss. The time-varying meshing stiffness is evaluated by means of a nonlinear finite element model, which allowed an accurate evaluation of the global and local teeth deformation in both directions: forward and reverse motions. Due to intentional tooth profile errors, e.g., profile modification, manufacturing error, or assembly error, the loaded and unloaded tooth contact analyses were conducted. The dynamic model was validated by comparisons with a verified SDOF model in terms of linear natural frequencies and nonlinear dynamic response. The present study provides amplitude frequency diagrams and bifurcation diagrams; for specific regimes, periodic, quasiperiodic, and chaotic responses were found. The dynamic behavior of the systems was evaluated using various tools such as modal analysis, nonlinear time series analysis, spectra, 3D-phase diagrams, and Poincaré maps. This study proves that decreasing the DOFs of the system can lose some dynamics. Different phenomena have been found such as trapping and boom-and-bust cycle. The dynamic response of different cases is evaluated by estimating the largest Lyapunov exponent and the correlation dimension. It is found that the system undergoes complex dynamic phenomena including nT-periodic, trapping, and aperiodic motions, which are evidenced in 3D-bifurcation diagrams, spectra, Poincaré maps, and 3D-phase diagrams. The chaotic motion found in this study is an undesirable behavior from a practical point of view, which can be avoided by adjusting the designed parameters. The results provide a basis for parameter design and dynamic characteristic control of the spiral bevel gear drive system.

Oil price shocks in the age of surging inflation

This study examines the nonlinear impact of oil price shocks on inflation in the euro area. We apply nonlinear vector time series models to identify regime shifts in recent times of geopolitical uncertainty. For the period from January 1999 to October 2022, we reveal the influence of geopolitical risks on exacerbating the inflationary impact of oil price shocks. Our impulse response analysis indicates that oil passthrough is more pronounced and persistent when the risks associated with adverse geopolitical events surpasses a given threshold. Eurozone inflation is found to be more vulnerable to geopolitical conflicts compared with the US economy. Our results underscore the nonlinear dynamic of oil price passthrough and the amplifying effect of geopolitical events that European policymakers should consider when addressing growing inflationary pressure.

Optimized hybrid ensemble learning approaches applied to very short-term load forecasting

The significance of accurate short-term load forecasting (STLF) for modern power systems’ efficient and secure operation is paramount. This task is intricate due to cyclicity, non-stationarity, seasonality, and nonlinear power consumption time series data characteristics. The rise of data accessibility in the power industry has paved the way for machine learning (ML) models, which show the potential to enhance STLF accuracy. This paper presents a novel hybrid ML model combining Gradient Boosting Regressor (GBR), Extreme Gradient Boosting (XGBoost), k-Nearest Neighbors (kNN), and Support Vector Regression (SVR), examining both standalone and integrated, coupled with signal decomposition techniques like STL, EMD, EEMD, CEEMDAN, and EWT. Through Automated Machine Learning (AutoML), these models are integrated and their hyperparameters optimized, predicting each load signal component using data from two sources: The National Operator of Electric System (ONS) and the Independent System Operators New England (ISO-NE), boosting prediction capacity. For the 2019 ONS dataset, combining EWT and XGBoost yielded the best results for very short-term load forecasting (VSTLF) with an RMSE of 1,931.8 MW, MAE of 1,564.9 MW, and MAPE of 2.54%. These findings highlight the necessity for diverse approaches to each VSTLF problem, emphasizing the adaptability and strength of ML models combined with signal decomposition techniques.

Nonlinear Autoregressive Neural Network for Forecasting COVID-19 Confirmed Cases in Malaysia

A nonlinear autoregressive neural network (NARNN) model is a feedforward neural network for handling complex nonlinear time series problem. In this study, the tangent sigmoid (tansig) activation function with different number of past values and different number of hidden neurons for NARNN model is determined. The COVID-19 daily confirmed cases in Malaysia are collected with different amount of sample used which are 100, 500 and 900. Therefore, data of 100, 500 and 900 days prior to 21 September 2022 are extracted for the NARNN model training, validation and testing procedure. The lowest average mean squared error (MSE) are considered as the best combination. Result shown that the past value 1:10 and number of neurons of 10 when the sample size is 100. At sample size 500, past values of 1:10 and number of neurons of 8 enables the model to perform at its best. Whereas for sample size 900, network setting of 1:5 past value and 5 hidden neurons gives the least MSE. Multi-step ahead time series forecasting is conducted to forecast the number of COVID-19 confirmed cases in 7 days which is from 22 to 28 September 2022. The result shown for 7-days-ahead confirmed cases forecasting Malaysia datasets, the best forecasting outcome occurs when 900 samples are inputted.

Flexible nonlinear inference and change-point testing of high-dimensional spectral density matrices

This paper studies a flexible approach to analyze high-dimensional nonlinear time series of unconstrained dimension based on linear statistics calculated from spectral average statistics of bilinear forms and nonlinear transformations of lag-window (i.e. band-regularized) spectral density matrix estimators. That class of statistics includes, among others, smoothed periodograms, nonlinear statistics such as coherency, long-run-variance estimators and contrast statistics related to factorial effects as special cases. Especially, we introduce the class of nonlinear spectral averages of the spectral density matrix. Having in mind big data settings, we study a sampling design which includes a sparse sampling scheme. Gaussian approximations with optimal rate are derived for nonlinear time series of growing dimension for these frequency domain statistics and the underlying lag-window (cross-) spectral estimator under non-stationarity. For change-testing (self-standardized) CUSUM statistics are examined. Further, a specific wild bootstrap procedure is proposed to estimate critical values. Simulation studies and an application to SP500 financial returns are provided in a supplement to this paper.

The Role of Public Debt in Economic Growth: An Empirical Analysis Evidence for Western Balkans and European Countries

Public debt was often considered as a supplementary source of public finances. In six Western Balkan states, a fixed regression model was employed to gauge the effect of public debt on economic growing using panel data. Findings demonstrate that public debt significantly affects economic growth. It was found too that direct foreign investments have a substantial influence into the economic growth. As an option for financing, state governments use external and internal public debt, which is often part of the debate approximately how much public debt should be used. Use of public debt varies from country to country and depends on economic growth and budgetary factors and economic and social demands. Reviewing the literature, it can be observed impact of public debt on overall economy and its growth and this was too used by states as an opportunity for economic growth. This is also reflected in the case of our study where we analyzed the data for EU member countries and Great Britain compared to the Western Balkans countries. During the research it is observed influence of public debt in economic growth on these countries and as such many states have exceeded the limits of the use of public debt based on legal frameworks, with the sole purpose of financing public demands and influence of economic growth. Public debt in this paper identifies the affiliation with economic growth through the specification of linear and non-linear time series models using the panel model for the years 2012-2021 for 35 countries in total. Also, the regression analysis shows us a support and correlation among public debt versus economic growth of countries part of this study. This is observed in developed countries, which have a higher potential and possibility of financing economic activity through public debt, while the Western Balkans countries are often challenged with the possibilities of financing from public debt. As variables we have GDP, Foreign Direct Investments and Inflation.

MSE model incorporating Fourier decomposition method: HRV study of ECG signals for atrial fibrillation and congestive heart failure

Traditional techniques to evaluate the complexity of biological signals forgo the numerous time scales present in such data. When these algorithms were applied to real-world datasets gathered in health and illness states, they produced inconsistent results. Sample entropy (SampEn) has been utilized extensively to evaluate the complexity of RR-interval time series. Using multi-scale Entropy analysis incorporating Sample Entropy, several research on the complexity of physiological signals have been conducted. The primary disadvantage of MSE is that coarse-graining results in a noticeable and considerable loss of information. For small scales, the method proves to be ineffective. So, for the MSE analysis of physiological data, we have employed the FDM rather than coarse-graining. This FDM, which is based on the Fourier theory, is excellent for studying nonlinear and nonstationary time series. This approach generates a TFE distribution that displays the data’s fundamental premise. This will provide a number of frequency bands with varying cut-off frequencies but consistent data across all of them. To further validate our suggested technique, we used “ANOVA analysis” to compare our results to the entropy analysis of a synthetic simulated database containing white noise (WN) and power noise (PN) signals.

Characterization of homogeneous nucleation of superheated liquid droplets by nonlinear analysis

The homogeneous bubble nucleation in superheated liquid droplets can be initiated by energetic particles or radiation. The nonlinearity in the heat transfer introduces chaos in the temperature time series of a boiling system. In the present study, the acoustical pulses from the homogeneous nucleation of superheated liquid droplets by neutrons and gamma-rays have been collected. Nonlinear time series analysis methods like 3D attractor reconstruction and Fast Fourier transformation (FFT) have been performed on the collected pulses. The analysis predicts the possibility of the existence of chaos, and the positive value of the largest Lyapunov exponent confirms it. The nonlinearity in the energy deposition by both the recoil nuclei and electrons from the neutrons and gamma-rays respectively, introduce chaos. A qualitative difference has been observed in the 3D attractor and Rescaled Range (R/S) plots between the neutron and gamma-ray-induced pulses, and the present differences are useful for the identification of these pulses.

Optimal combination weight interval-valued carbon price forecasting model based on adaptive decomposition method

Accurate carbon price predictions are of utmost significance in curbing greenhouse gas emissions and advancing environmentally sustainable, low-carbon development. As carbon price time series are influenced by time intervals, point value predictions often fall short in capturing the inherent variability within these intervals. Hence, this paper introduces an interval decomposition and integration framework for carbon price prediction based on the interval feedback variational mode decomposition (IFVMD) algorithm and the optimal combination weight prediction model. First, the IFVMD algorithm decomposes the inverted interval-valued sequence through a self-adaptive determination of the decomposition mode number. It then restructures the decomposed modes into interval trends and residuals, scientifically reducing data volatility. Subsequently, within the proposed optimal combination weight model, the Cuckoo Search Optimization algorithm is employed to calculate the weights of subsequences predicted by two models, which merges model features and realizes model complementation. Finally, the results of the prediction are derived by reconstructing the trend and residual interval. The Interval Mean Absolute Percentage Errors (IMAPE) of the model's prediction results are 2.3754%, 3.3773%, and 3.2169%, respectively. These values indicate that the proposed interval combination forecasting technique demonstrates excellent prediction accuracy and stability, and the performance of the proposed model is superior compared to the baseline models. This optimal combination strategy has been proven to be an effective approach for forecasting nonlinear interval-based carbon price time series.

Multiview collaboration learning classification model of stock data based on view weighting mechanism

Machine learning methods have become an effective strategy commonly used in quantitative hedge funds, which can maximize profits and reduce investment risks to a certain extent. Traditional stock forecasting systems are usually based on a single attribute of stock data. There are two main challenges in this process: 1) Use suitable processing methods to deal with highly nonlinear time series data such as stocks. 2) Using a single class of stock data for training does not capture the correlation between other related data and the training data. Based on RBF neural network, this research introduces view weighting and collaborative learning mechanism, and proposes a MV-RBF model. It mainly includes the following contributions: 1) By comparing the experimental results of MV-RBF model with the single-view model, its effectiveness and feasibility are verified. 2) The MV-RBF model was compared with other commonly used classification models to analyze its advantages and disadvantages. 3) Study the relevant parameters, stability and other indicators of MV-RBF model. The experimental results show that compared with the single view model and most common classification models, MV-RBF has certain improvement in the prediction accuracy.

Predicting the Long-Term Dependencies in Time Series Using Recurrent Artificial Neural Networks

Long-term dependence is an essential feature for the predictability of time series. Estimating the parameter that describes long memory is essential to describing the behavior of time series models. However, most long memory estimation methods assume that this parameter has a constant value throughout the time series, and do not consider that the parameter may change over time. In this work, we propose an automated methodology that combines the estimation methodologies of the fractional differentiation parameter (and/or Hurst parameter) with its application to Recurrent Neural Networks (RNNs) in order for said networks to learn and predict long memory dependencies from information obtained in nonlinear time series. The proposal combines three methods that allow for better approximation in the prediction of the values of the parameters for each one of the windows obtained, using Recurrent Neural Networks as an adaptive method to learn and predict the dependencies of long memory in Time Series. For the RNNs, we have evaluated four different architectures: the Simple RNN, LSTM, the BiLSTM, and the GRU. These models are built from blocks with gates controlling the cell state and memory. We have evaluated the proposed approach using both synthetic and real-world data sets. We have simulated ARFIMA models for the synthetic data to generate several time series by varying the fractional differentiation parameter. We have evaluated the proposed approach using synthetic and real datasets using Whittle’s estimates of the Hurst parameter classically obtained in each window. We have simulated ARFIMA models in such a way that the synthetic data generate several time series by varying the fractional differentiation parameter. The real-world IPSA stock option index and Tree Ringtime series datasets were evaluated. All of the results show that the proposed approach can predict the Hurst exponent with good performance by selecting the optimal window size and overlap change.

A prospective study: Advances in chaotic characteristics of serum Raman spectroscopy in the field of assisted diagnosis of disease

Chaos theory is an important branch of mathematics and its theory has been widely applied in many fields such as physics and medicine. Based on existing spectroscopic techniques, this paper used chaos theory as a research method for nonlinear time series to analyze Raman spectral time domain curves in order to improve the performance of disease diagnostic models and explore a new paradigm of spectroscopic technology for intelligent assisted disease diagnosis. We quantitatively identified the chaotic characteristics of time domain Raman spectra by three methods, extracted chaotic features such as correlation dimension and Kolmogorov entropy, and used the chaotic features as input to Extreme Learning Machine (ELM), Back Propagation Neural Network (BPNN), K-Nearest Neighbor (KNN) and Support Vector Machine (SVM) to diagnose patients with lung cancer (LC), glioma, renal cell carcinoma (RCC) and esophageal cancer (EC). The Raman spectra were also analyzed by traditional spectral feature extraction & modelling method, and the results of traditional spectral feature extraction & modelling method and chaotic feature modelling method were compared. The experimental results showed that the extraction of effective chaotic features in the full spectral range could achieve comparable diagnostic results with the traditional spectral feature extraction & modelling method. To further validate the effectiveness of chaos theory in Raman spectral data, the full spectrum was divided into three consecutive subsequences of 500–1000, 1000–1500, and 1500–2000 cm−1, and the above experimental steps were repeated respectively, and the results of the traditional spectral feature extraction & modelling method and chaotic feature modelling were compared. The results showed that as the spectral range was split into consecutive subsequences, the diagnostic performance of the chaotic features in each subsequence performed better than that of conventional spectral analysis techniques. In this study, the technique bridges the gap in the application of chaotic signals to Raman spectroscopy techniques, focuses on global features in the time domain profile of Raman spectra, and demonstrates the significant value of chaos theory in artificial intelligence-assisted spectroscopic medical diagnosis.

A novel time-delay neural grey model and its applications

Grey system theory uses differential equations to model small sample time series to predict the short-term development law of things in the future. Since the most classical GM(1, 1) model was proposed, many scholars have improved it and derived various grey models that can predict linear or nonlinear time series. However, the existing grey models are still not accurate enough for constructing background values and parameter estimation methods. In order to improve the accuracy and applicability of the grey model, a novel neural grey model with accumulated time delays is proposed in this paper. In this model, the whitening equation of the grey model is constructed by combining the long short-term memory network to add time-delay variables to the original grey model. Second, the neural ordinary differential equation (NODE) is used to train the model to determine the time delays, the time-delay weights, and the model parameters to obtain better predictions. Finally, the Euler method is used to get the final prediction series. The new model’s performance is tested through experiments on energy consumption and CO2 emissions prediction. The results were compared with some grey models, support vector regression (SVR), and autoregressive integrated moving average models (ARIMA). It can be concluded that the new model has better generalization performance and higher prediction accuracy than the selected comparative models.

Nexus between renewable energy and economic growth in G7 countries: New insight from nonlinear time series and panel cointegration analysis

This study aims to investigate the impact of renewable energy consumption on the economic growth of G7 countries and explore the potential nonlinear relationship between the two variables. Initially, the NARDL model is employed to analyze the G7 countries, allowing for the control of nonlinear relationships and considering asymmetric effects. The findings of the NARDL model reveal an asymmetric long run cointegration relationship between renewable energy consumption and economic growth in Canada and the US, while other countries show different dynamics. Subsequently, a causal dynamic impact analysis is conducted to gain further insights into the relationship between renewable energy consumption and economic growth. In the next step, the advantage of panel data analysis is utilized to investigate the overall impact across all G7 countries. For this purpose, the study extends the NARDL model to the PNARDL (Panel Nonlinear Autoregressive Distributed Lag) model, which facilitates the control of asymmetric effects and nonlinearity in the panel data model. In this context, this study is one of the first studies to control the nonlinearity in panel data analysis. The results from the PNARDL model demonstrate that renewable energy has a positive long-term relationship with economic growth in G7 countries; however, this relationship is statistically insignificant.

An ecological network approach for detecting and validating influential organisms for rice growth.

How to achieve sustainable food production while reducing environmental impacts is a major concern in agricultural science, and advanced breeding techniques are promising for achieving such goals. However, rice is usually grown under field conditions and influenced by surrounding ecological community members. How ecological communities influence the rice performance in the field has been underexplored despite the potential of ecological communities to establish an environment-friendly agricultural system. In the present study, we demonstrate an ecological-network-based approach to detect potentially influential, previously overlooked organisms for rice (Oryza sativa). First, we established small experimental rice plots, and measured rice growth and monitored ecological community dynamics intensively and extensively using quantitative environmental DNA metabarcoding in 2017 in Japan. We detected more than 1000 species (including microbes and macrobes such as insects) in the rice plots, and nonlinear time series analysis detected 52 potentially influential organisms with lower-level taxonomic information. The results of the time series analysis were validated under field conditions in 2019 by field manipulation experiments. In 2019, we focused on two species, Globisporangium nunn and Chironomus kiiensis, whose abundance was manipulated in artificial rice plots. The responses of rice, namely, the growth rate and gene expression patterns, were measured before and after the manipulation. We confirmed that, especially in the G. nunn-added treatment, rice growth rate and gene expression pattern were changed. In the present study, we demonstrated that intensive monitoring of an agricultural system and the application of nonlinear time series analysis were helpful to identify influential organisms under field conditions. Although the effects of the manipulations were relatively small, the research framework presented here has future potential to harness the ecological complexity and utilize it in agriculture. Our proof-of-concept study would be an important basis for the further development of field-basis system management.

An ecological network approach for detecting and validating influential organisms for rice growth

How to achieve sustainable food production while reducing environmental impacts is a major concern in agricultural science, and advanced breeding techniques are promising for achieving such goals. However, rice is usually grown under field conditions and influenced by surrounding ecological community members. How ecological communities influence the rice performance in the field has been underexplored despite the potential of ecological communities to establish an environment-friendly agricultural system. In the present study, we demonstrate an ecological-network-based approach to detect potentially influential, previously overlooked organisms for rice (Oryza sativa). First, we established small experimental rice plots, and measured rice growth and monitored ecological community dynamics intensively and extensively using quantitative environmental DNA metabarcoding in 2017 in Japan. We detected more than 1000 species (including microbes and macrobes such as insects) in the rice plots, and nonlinear time series analysis detected 52 potentially influential organisms with lower-level taxonomic information. The results of the time series analysis were validated under field conditions in 2019 by field manipulation experiments. In 2019, we focused on two species, Globisporangium nunn and Chironomus kiiensis, whose abundance was manipulated in artificial rice plots. The responses of rice, namely, the growth rate and gene expression patterns, were measured before and after the manipulation. We confirmed that, especially in the G. nunn-added treatment, rice growth rate and gene expression pattern were changed. In the present study, we demonstrated that intensive monitoring of an agricultural system and the application of nonlinear time series analysis were helpful to identify influential organisms under field conditions. Although the effects of the manipulations were relatively small, the research framework presented here has future potential to harness the ecological complexity and utilize it in agriculture. Our proof-of-concept study would be an important basis for the further development of field-basis system management.

Estimation of prediction error in time series

Summary The accurate estimation of prediction errors in time series is an important problem, which has immediate implications for the accuracy of prediction intervals as well as the quality of a number of widely used time series model selection criteria such as the Akaike information criterion. Except for simple cases, however, it is difficult or even impossible to obtain exact analytical expressions for one-step and multi-step predictions. This may be one of the reasons that, unlike in the independent case (see Efron, 2004), up to now there has been no fully established methodology for time series prediction error estimation. Starting from an approximation to the bias-variance decomposition of the squared prediction error, a method for accurate estimation of prediction errors in both univariate and multivariate stationary time series is developed in this article. In particular, several estimates are derived for a general class of predictors that includes most of the popular linear, nonlinear, parametric and nonparametric time series models used in practice, with causal invertible autoregressive moving average and nonparametric autoregressive processes discussed as lead examples. Simulations demonstrate that the proposed estimators perform quite well in finite samples. The estimates may also be used for model selection when the purpose of modelling is prediction.