Nonlinear Time Series Research Articles

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.

Earthquake alerting based on spatial geodetic data by spatiotemporal information transformation learning

Alerting for imminent earthquakes is particularly challenging due to the high nonlinearity and nonstationarity of geodynamical phenomena. In this study, based on spatiotemporal information (STI) transformation for high-dimensional real-time data, we developed a model-free framework, i.e., real-time spatiotemporal information transformation learning (RSIT), for extending the nonlinear and nonstationary time series. Specifically, by transforming high-dimensional information of the global navigation satellite system into one-dimensional dynamics via the STI strategy, RSIT efficiently utilizes two criteria of the transformed one-dimensional dynamics, i.e., unpredictability and instability. Such two criteria contemporaneously signal a potential critical transition of the geodynamical system, thereby providing early-warning signals of possible upcoming earthquakes. RSIT explores both the spatial and temporal dynamics of real-world data on the basis of a solid theoretical background in nonlinear dynamics and delay-embedding theory. The effectiveness of RSIT was demonstrated on geodynamical data of recent earthquakes from a number of regions across at least 4 y and through further comparison with existing methods.

Prediction of roll wear and thermal expansion based on informer network in hot rolling process and application in the control of crown and thickness

The inaccuracy of roll thermal expansion and roll wear settings affects strip steel plate shape and thickness in hot-rolling process. Roll wear and thermal expansion are nonlinear time series that cannot be neglected in the roll engineering. In order to make up for the shortcomings of the existing models, a novel prediction model of roll thermal expansion and roll wear based on Informer is developed. Firstly, multiple experiments are conducted to determine hyperparameter such as training epoch, dropout, batch size and learning rate. Then, the predicted results of finishing mill group (F1–F7 stand) are compared with the long-short-term memory (LSTM) model, the artificial neural network (ANN) model and the recurrent neural network (RNN) model. The results show that the model based on Informer network has highly accurate in predicting roll thermal expansion and roll wear. Finally, the application results show that the hit rate is 98.412 % within the tolerance range ± 4 μm and the hit rate within the ±40 μm thickness tolerance deviation range reach 98.94 % which proves that the roll wear and thermal expansion model based on Informer has outstanding advantages in the hot rolling shape control system.

Horizontal Divide and Conquer Methods for Non-Linear Time Series Forecasting Using LSTM-ANN; a Comparative Study Based on Simulated Data

Horizontal Divide and Conquer Methods for Non-Linear Time Series Forecasting Using LSTM-ANN; a Comparative Study Based on Simulated Data

Nonlinear Time Series Analysis and Prediction of General Aviation Accidents Based on Multi-Timescales

General aviation accidents have complex interactions and influences within them that cannot be simply explained and predicted by linear models. This study is based on chaos theory and uses general aviation accident data to conduct research on different timescales (HM-scale, ET-scale, and EF-scale). First, time series are constructed by excluding seasonal patterns from the statistics of general aviation accidents. Secondly, the chaotic properties of multi-timescale series are determined by the 0–1 test and Lyapunov exponent. Finally, by introducing the sparrow search algorithm and tent chaotic mapping, a CSSA-LSSVM prediction model is proposed. The accident data of the National Transportation Safety Board (NTSB) of the United States in the past 15 years is selected for case analysis. The results show that the phase diagram of the 0–1 test presents Brownian motion characteristics, and the maximum Lyapunov exponents of the three scales are all positive, proving the chaotic characteristics of multi-timescale series. The CSSA-LSSVM prediction model’s testing results illustrate its superiority in time series predicting, and when the timescale declines, the prediction error reduces gradually while the fitting effect strengthens and then decreases. This study uncovers the nonlinear chaotic features of general aviation accidents and demonstrates the significance of multi-timescale research in time series analysis and prediction.

Forecasting Day-Ahead Brent Crude Oil Prices Using Hybrid Combinations of Time Series Models

Crude oil price forecasting is an important research area in the international bulk commodity market. However, as risk factors diversify, price movements exhibit more complex nonlinear behavior. Hence, this study provides a comprehensive analysis of forecasting Brent crude oil prices by comparing various hybrid combinations of linear and nonlinear time series models. To this end, first, the logarithmic transformation is used to stabilize the variance of the crude oil prices time series; second, the original time series of log crude oil prices is decomposed into two new subseries, such as a long-run trend series and a stochastic series, using the Hodrick–Prescott filter; and third, two linear and two nonlinear time series models are considered to forecast the decomposed subseries. Finally, the forecast results for each subseries are combined to obtain the final day-ahead forecast result. The proposed modeling framework is applied to daily Brent spot prices from 1 January 2013 to 27 December 2022. Six different accuracy metrics, pictorial analysis, and a statistical test are performed to verify the proposed methodology’s performance. The experimental results (accuracy measures, pictorial analysis, and statistical test) show the efficiency and accuracy of the proposed hybrid forecasting methodology. Additionally, our forecasting results are comparatively better than the benchmark models. Finally, we believe that the proposed forecasting method can be used for other complex financial time data to obtain highly efficient and accurate forecasts.

Ensemble learning-based nonlinear time series prediction and dynamic multi-objective optimization of organic rankine cycle (ORC) under actual driving cycle

Complicated road conditions make organic Rankine cycle (ORC) operation characteristics show hysteresis and uncertainty. Under the strong coupling correlation of many operating parameters, how to realize the dynamic optimization of ORC comprehensive performance is the key to obtain practical application potential. Based on ensemble learning mechanism, neural network modeling, ensemble system, unsupervised learning, partial mutual information and optimization algorithm are integrated. This paper presents a nonlinear time series prediction and dynamic multi-objective optimization scheme. The average accuracy increased by at least 59.6%. Taking the thermodynamic performance and environmental impact as optimization objectives, dynamic multi-objective optimization is carried out under road conditions. The optimization scheme can effectively trade off the nonlinear correlation between thermal efficiency and emissions of CO2 equivalent.

Modeling and forecasting electricity consumption amid the COVID-19 pandemic: Machine learning vs. nonlinear econometric time series models

Accurately modeling and forecasting electricity consumption remains a challenging task due to the large number of the statistical properties that characterize this time series such as seasonality, trend, sudden changes, slow decay of autocorrelation function, among many others. This study contributes to this literature by using and comparing four advanced time series econometrics models, and four machine learning and deep learning models11These models include the autoregressive model with seasonality, autoregressive models with exogenous variables, the autoregressive fractionally integrated moving average model with exogenous variables, the three state autoregressive Markov switching model with exogenous variable, Prophet, EXtreme Gradient Boosting, Long-Short-Term Memory and Support Vector Regression. to analyze and forecast electricity consumption during COVID-19 pre-lockdown, lockdown, releasing-lockdown, and post-lockdown phases. Monthly data on Qatar’s total electricity consumption has been used from January 2010 to December 2021. The empirical findings demonstrate that both econometric and machine learning models are able to capture most of the important statistical features characterizing electricity consumption. In particular, it is found that climate change based factors, e.g temperature, rainfall, mean sea-level pressure and wind speed, are key determinants of electricity consumption. In terms of forecasting, the results indicate that the autoregressive fractionally integrated moving average and the three state autoregressive Markov switching models with exogenous variables outperform all other models. Policy implications and energy-environmental recommendations are proposed and discussed.