Nonstationary Time Series Research Articles

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.

Research on Cloud Platform Software Aging Prediction Method Based on VMD-ARIMA-BilSTM Combined Model

When the cloud platform runs under heavy load for a long time, internal resources will be consumed and errors will accumulate continuously. As a result, the software aging phenomenon occurs, which ultimately degrades the performance and reliability of the software system. Aiming at the above problems, this paper proposes a hybrid model based on integrated variational mode decomposition, moving average free regression and long and short memory network (VMD-ARIMA-BILSTM) to predict the software aging problem. Firstly, the original resource utilization rate is decomposed into stationary time series and non-stationary time series by variational mode decomposition. Then, the advantages of moving average free regression and bidirectional long short-term memory network are used to predict stationary and non-stationary series respectively. Finally, the prediction results are reconstructed to obtain the final prediction results. Experimental results show that compared with single ARIMA and BI-LSTM, the hybrid model designed in this paper has higher prediction accuracy and faster convergence speed.

Analyzing and Predicting Temperature Data in Baoji: A SARIMA Model Approach

In this study, I analyzed and predicted the temperature data of Baoji. First, I processed the data with outliers and explored the seasonal variation pattern of the temperature data through seasonal decomposition. Through the ADF unit root test, I confirm that the temperature data are non-stationary time series. To make the prediction, I built the SARIMA model and adjusted the model parameters to get the best performance. I tried different autoregressive orders, difference orders, moving average orders, and seasonal periods, and selected the optimal model by comparing the model fitting effect and prediction ability. Finally, I made a temperature prediction for some time in the future based on the SARIMA model I built. The forecast results show that the temperature shows a gradually increasing trend in the given time range. This conclusion is based on my evaluation of the model and analysis of the predicted results. Although I have achieved some useful results through the analysis and prediction of temperature data, there are still some limitations to this study. The method of handling outliers in the data processing stage may need further improvement to improve the accuracy of the data. In addition, I only used the SARIMA model for the prediction, and the application of other time series models may yield more accurate results. In summary, this study predicted the temperature data through time series analysis and SARIMA model and came to the conclusion that the temperature gradually increased. Future research can be carried out from the aspects of improving data processing methods and applying more time series models to improve the accuracy and reliability of temperature prediction.

Multicriteria decision support employing adaptive prediction in a tensor-based feature representation

Multicriteria decision analysis (MCDA) is a widely used tool to support decisions in which a set of alternatives should be ranked or classified based on multiple criteria. Recent studies in MCDA have shown the relevance of considering not only current evaluations of each criterion but also past data. Past-data-based approaches carry new challenges, especially in time-varying environments. This study deals with this challenge via essential tools of signal processing, such as tensorial representations and adaptive prediction. More specifically, we structure the criteria’ past data as a tensor and, by applying adaptive prediction, we compose signals with these prediction values of the criteria. Besides, we transform the prediction in the time domain into a most favorable decision making domain, called the feature domain. We present a novel extension of the MCDA method PROMETHEE II, aimed at addressing the tensor in the feature domain to obtain a ranking of alternatives. Numerical experiments were performed using real-world time series, and our approach is compared with other existing strategies. The results highlight the relevance and efficiency of our proposal, especially for nonstationary time series.

Cumulative Diversity Pattern Entropy (CDEn): A High-Performance, Almost-Parameter-Free Complexity Estimator for Nonstationary Time Series

Tedious parameter settings and poor performances seriously affect the entropy estimation's effectiveness in time series analysis. To solve these limits, we propose a conceptually novel definition, cumulative diversity pattern entropy (CDEn), focusing on eliminating parameter selections and improving quantization accuracy, stability, and robustness. The CDEn algorithm consists of three steps: (1) improved phase-space reconstruction (IPSR) with constant embedding dimension <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${\bm{m\ }} = {\bm{\ }}2$</tex-math></inline-formula> and time delay <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${\bm{\tau \ }} = {\bm{\ }}1$</tex-math></inline-formula> ; (2) diversity pattern partition generated by the cosine similarity between adjacent vectors; and (3) entropy calculation based on the normalized cumulative probability distribution. Numerical experiments are performed using 7 synthetic datasets and 15 baseline entropy methods for comparative validation. The results confirm CDEn's best description of chaotic/stochastic dynamics with the highest quantization accuracy and the lowest error rate of 2.04%. The coefficient of variation (CV) results also verify CDEn's excellent quantization stability with CV lower than 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-2</sup> . The relative change rate (RCR) results demonstrate that CDEn achieves the best robustness to data length and noise. Finally, the entropy algorithms are applied to a real-world dataset, i.e., neonatal sleep EEG analysis. The results further confirm that suggested CDEn outperforms the state-of-the-art entropy methods, with the minimum outliers and best statistical significance (highest mean of effect size, 1.22) in characterizing the neurodynamics of different sleep stages.

Analysis of the stationarity and correlation of the global temperature and carbon dioxide time series

Background: The rapid and ongoing phenomenon of global warming has negatively impacted both the Earth’s environment and its inhabitants. Time series and regression analysis techniques play a significant role in weather forecasting and the interpretation of climate data. One of the key characteristics of time series analysis is stationarity. Methods: In this article, we explore how detrending and differencing techniques can be used to transform the time series of global temperature and carbon dioxide into stationary series. Regression models and goodness of fit tests were used to examine the relationship between carbon dioxide and data on global temperature. A cross-correlation time series model is also used to assess those time series’ lagging and leading characteristics. Results: The study of data on global temperature anomalies indicates that detrending and differencing are helpful in transforming temperature time series into stationary time series. However, the first differencing and detrending methods do not make the carbon dioxide time series stationary; instead, an alternate transformation is needed. Neither the carbon dioxide time series nor the global temperature time series lag or lead with regard to the cross-correlation function. Conclusions: In this article, we looked into stationarity and some other topics associated with correlation in terms of data on CO2 and global temperature. Stationarity is one of the important properties to check before conducting a more thorough investigation of the time series. To transform a non-stationary time series into a stationary one, there are numerous techniques available. However, in this article, we just pay attention to detrending and differencing and how those methods perform with respect to time series data for global temperature and carbon dioxide.

Nonstationary time series change direction forecast method using improved leading indicator

AbstractThis paper presents a method for forecasting the change direction of nonstationary time series using the improved leading indicator. The leading indicator is a method developed by Ehlers that translates a time series mathematically in the future direction with respect to the time axis and calculates the leading value of the time series. However, this method has the problem that the leading value can be calculated only in the low frequency region with a normalized frequency of 0.06 or more (normalized period of 17 or more) at the maximum. In order to solve this problem, by the gentle slope the amplitude characteristics in the low frequency region of the leading indicator, it is possible to calculate the leading value in the frequency domain with a normalized frequency of 0.25 or more (normalized period of four or more) at the maximum. By applying the preceding value to the instantaneous periodic time series by the improved sine wave indicator developed by Ehlers, it is possible to forecast the change direction of the non‐stationary time series in the short term.

Denoising gravitational-wave signals from binary black holes with a dilated convolutional autoencoder

Abstract The broadband frequency output of gravitational-wave (GW) detectors is a non-stationary and non-Gaussian time series data stream dominated by noise populated by local disturbances and transient artifacts, which evolve on the same timescale as the GW signals and may corrupt the astrophysical information. We study a denoising algorithm dedicated to expose the astrophysical signals by employing a convolutional neural network in the encoder-decoder configuration, i.e. apply the denoising procedure of coalescing binary black hole signals to the publicly available LIGO O1 time series strain data. The denoising convolutional autoencoder neural network is trained on a dataset of simulated astrophysical signals injected into the real detector’s noise and a dataset of detector noise artifacts (‘glitches’), and its fidelity is tested on real GW events from O1 and O2 LIGO-Virgo observing runs.

Phase synchronization in cryptocurrency network and its features

Investigating the time–frequency-based phase synchronization between nonstationary time series of the cryptocurrencies’ prices can be a suitable tool to reveal their complicated interactions at different frequencies. In this work, the phase synchronization between 25 cryptocurrencies with the highest capitalization from December 1, 2021 to June 1, 2022 is calculated using the phase-locking value method based on wavelet transform. Then, utilizing the graph theory, the cryptocurrency networks are constructed, and their topological features like path length (PL), clustering coefficient (CC) and node strength are evaluated in various frequencies. This research indicates a strong phase synchronization between the investigated cryptocurrencies, especially in low frequencies. Also, the networks’ high average CC and short PL compared to their equivalent regular and random networks display the small-worldness of the networks. We observe from the obtained results that Bitcoin, Ethereum and Binance currencies, among the most popular cryptocurrencies, have the highest average node strengths at different frequencies. Also, TRON shows the lowest CC and node strength among all currencies, representing its limited phase interaction with other currencies.

Tractable Maximum Likelihood Estimation for Latent Structure Influence Models With Applications to EEG &amp; ECoG Processing

Brain signals are nonlinear and nonstationary time series, which provide information about spatiotemporal patterns of electrical activity in the brain. CHMMs are suitable tools for modeling multi-channel time-series dependent on both time and space, but state-space parameters grow exponentially with the number of channels. To cope with this limitation, we consider the influence model as the interaction of hidden Markov chains called Latent Structure Influence Models (LSIMs). LSIMs are capable of detecting nonlinearity and nonstationarity, making them well suited for multi-channel brain signals. We apply LSIMs to capture the spatial and temporal dynamics in multi-channel EEG/ECoG signals. The current manuscript extends the scope of the re-estimation algorithm from HMMs to LSIMs. We prove that the re-estimation algorithm of LSIMs will converge to stationary points corresponding to Kullback-Leibler divergence. We prove convergence by developing a new auxiliary function using the influence model and a mixture of strictly log-concave or elliptically symmetric densities. The theories that support this proof are derived from previous studies by Baum, Liporace, Dempster, and Juang. We then develop a closed-form expression for re-estimation formulas using tractable marginal forward-backward parameters defined in our previous study. Simulated datasets and EEG/ECoG recordings confirm the practical convergence of the derived re-estimation formulas. We also study the use of LSIMs for modeling and classification on simulated and real EEG/ECoG datasets. Based on AIC and BIC, LSIMs perform better than HMMs and CHMMs in modeling embedded Lorenz systems and ECoG recordings. LSIMs are more reliable and better classifiers than HMMs, SVMs and CHMMs in 2-class simulated CHMMs. EEG biometric verification results indicate that the LSIM-based method improves the area under curve (AUC) values by about 6.8% and decreases the standard deviation of AUC values from 5.4% to 3.3% compared to the existing HMM-based method for all conditions on the BED dataset.

Forecasting the influx of crime cases using seasonal autoregressive integrated moving average model

Crime constitutes a profound challenge to the societal fabric of a nation and often finds its roots in factors such as avarice, destitution, and economic adversity. This study endeavors to proactively address the issue of crime through the employment of a crime forecasting model, aimed at uncovering latent correlations and underlying patterns. Specifically, it employs the Seasonal Autoregressive Integrated Moving Average (SARIMA) model to project the future incidence of criminal cases. The research objectives encompass forecasting crime case numbers through time series analysis, appraising the statistical significance of monthly crime occurrences, and assessing the crime dataset utilizing the MATLAB Econometric Modeler. Leveraging historical crime data spanning from January 2018 to December 2021, sourced from nineteen municipalities in Negros Occidental, Philippines, forms the basis for crime case forecasting. An autoregressive test is applied to ascertain the acceptable confidence interval and goodness of fit for crime occurrences. Furthermore, MATLAB Econometric Modeler employs the Ljung-Box test to differentiate between stationary and non-stationary time series and residual crime cases. Notably, the study reveals a significant cyclic pattern in crime cases occurring every 20 months, underscoring the imperative for targeted crime prevention interventions. This study underscores the necessity for consistent and robust law enforcement measures by local government units across the nineteen municipalities in Negros Occidental, focusing on the five identified categories of criminal cases. It is recommended that these measures be implemented diligently to mitigate crime occurrences in the subsequent twenty-first month. Moreover, the study holds potential for extension to regions grappling with elevated crime rates due to inadequate control strategies in place.

Time Series Multi-Step Forecasting Based on Memory Network for the Prognostics and Health Management in Freight Train Braking System

In rail trains, the prognostics and health management system will make use of data from sensors deployed in key components. These data are typically non-stationary multi-variable time series with abrupt variations. The challenges of multivariate time series forecasting include how to identify the interactions between various variables, and how to assess the influence of historical data on present data. This paper presents the nature of the air brake system and its physical models. By analyzing the observed data obtained from the freight train air brake system, a Memory network-based Time series Multi-step fault Forecasting model (MTMF) is proposed. MTMF consists of a dual-encoder and a memory network module for feature extraction. The two encoders are used to extract features of short-term and long-term historical data respectively. The memory network is used to further mine the different weights of the long-term historical data. MTMF also designs a joint multi-step forecasting loss function, which is composed of shape, time and mean square error losses between the forecasting series and the real series. The improved loss function is no longer restricted to the differences in evaluation points. MTMF is evaluated on the real freight train braking system time series dataset. The results show that MTMF outperforms other forecasting methods on multivariate time series. The forecasting accuracy is increased by 5%-45%, demonstrating that the model is effective for non-stationary series and can better mine the dependence patterns for the train braking system.

Graphical models for nonstationary time series

Graphical models for nonstationary time series

Prediction Model of Horizontal Drilling Trajectory of Anti-collision Drilling Robot

The horizontal drilling trajectory of the anti-collision drilling robot is taken as the research object and its drilling trajectory prediction model is established in this paper. The drilling trajectory is affected by many factors, such as the structural parameters of the auger, the drill bit, the drilling process parameters, and the geological characteristics of the coal seam, etc., which results in the existence of multi-level time-scale structure and localization characteristics of the drilling trajectory data in the time domain. The wavelet analysis method can decompose the relatively complex non-stationary time series problem into low-frequency decomposition signals representing trend items and high-frequency decomposition signals representing periodicity and randomness. It can not only predict the main trend of drilling trajectory changes but also effectively predict sudden load changes and short-term changes. Based on this, a new prediction method is proposed in this paper. Firstly, the data is decomposed into relatively simple component signals using wavelet decomposition technology, then the prediction models are established according to the characteristics of each component signal. Finally, the drilling trajectory prediction model is established by synthesizing the prediction results. The anti-impact drilling robot drilling test bed is set up and the drilling experiments are carried out to verify the effectiveness of the model, which can lay the foundation for the anti-impact drilling robot drilling deflection control.

Prediksi Spot Price Komoditas Emas Berjangka dengan Pendekatan Vector Error Correction Model

Time series data usually exhibit non-stationary behavior and involve interrelated variables. Thus, we need a model that can obtain good forecasting results from non-stationary time series data with multivariate variables. The Vector Error Correction Model (VECM) is a multivariate time series model which is a vector form of Vector Autoregressive Regression (VAR) for time series data that are non-stationary and have a cointegration relationship. This research was conducted to model the cointegration relationship in providing clarity on the long-term relationship of the influence of future prices and the Covid-19 pandemic on price movements of gold futures commodities and to predict spot price prediction modeling for gold futures commodities. The results of the research using the VECM (2) model, which is the best model, show that the future price of the gold commodity is quite dominant in influencing the value of the spot price of gold. The Covid-19 variable does not have a significant effect on the spot gold price variable.

Change points detection for nonstationary multivariate time series

Change points detection for nonstationary multivariate time series

Under-reported time-varying MINAR(1) process for modeling multivariate count series

A time-varying multivariate integer-valued autoregressive of order one (tvMINAR(1)) model is introduced for the non-stationary time series of correlated counts when under-reporting is likely present. A non-diagonal autoregression probability network is structured to preserve the cross-correlation of multivariate series, provide a necessary condition to ease model-fittings computations, and derive the full likelihood using the Viterbi algorithm. The motivating construction applies to fully under-reported counts that rely on a mixture presentation of the random thinning operator. Simulation studies are conducted to examine the proposed model, and the analysis of COVID-19 daily cases is accomplished to highlight its usefulness in applications. Finally, the comparison of models is presented using the posterior predictive checking method.

Adaptive Template Reconstruction for Effective Pattern Classification.

A novel instance-based algorithm for pattern classification is presented and evaluated in this paper. This new method is motivated by the challenge of pattern classifications where only limited and/or noisy training data are available. For every classification, the proposed system transforms the query data and the training templates based on their distributions in the feature space. One of the major novelties of the proposed method is the concept of template reconstruction enabling improved performance with limited training data. The technique is compared with similar algorithms and evaluated using both the image and time-series modalities to demonstrate its effectiveness and versatility. Two public image databases, FASHION-MNIST and CIFAR-10, were used to test its effectiveness for the classification of images using small amounts of training samples. An average classification improvement of 2~3% was observed while using a small subset of the training database, compared to the performances achieved by state-of-the-art techniques using the full datasets. To further explore its capability in solving more challenging classification problems such as non-stationary time-series electroencephalography (EEG) signals, a clinical grade 64-electrode EEG database, as well as a low-quality (high-noise level) EEG database, obtained using a low-cost system equipped with a single dry sensor, have also been used to test the algorithm. Adaptive reconstruction of the feature instances has been seen to have substantially improved class separation and matching performance for both still images and time-series signals. In particular, the method is found to be effective for the classification of noisy non-stationary data with limited training data volumes, indicating its potential suitability for a wide range of applications.

Time series analysis model for forecasting unsteady electric load in buildings

Accurate and reliable load forecasting is crucial for ensuring the security and stability of the power grid. This paper proposes a combined prediction method based on Empirical Wavelet Transform (EWT) and Autoformer time series prediction model for the non-stationary and non-linear time series of electric load. The original sequence is first decomposed by EWT to obtain a set of stable subsequences, and then the Autoformer time series prediction model is used to predict each subsequence. Finally, the prediction results of each subsequence are combined to obtain the final prediction results. The proposed EWT-Autoformer prediction model is applied to an electric load example, and the experimental results are compared with the Recurrent Neural Network (RNN) method, Long Short-Term Memory (LSTM) method, and Informer method under the same conditions. The experimental results indicate that compared to LSTM, the method proposed in the paper has an R2 improvement of 9–20 percentage points, an improvement of 6–8 percentage points compared to RNN, an improvement of 3–7 percentage points compared to Informer, and an improvement of 2–3 percentage points compared to Autoformer. In addition, the RMSE and MAE are also significantly lower than other models.

Robust sequential online prediction with dynamic ensemble of multiple models: A review

The use of time series for sequential online prediction (SOP) has long been a research topic, but achieving robust and computationally efficient SOP with non-stationary time series remains a challenge. This paper reviews a framework, called Bayesian Dynamic Ensemble of Multiple Models (BDEMM), which addresses SOP in a theoretically elegant way, and have found widespread use in various fields. BDEMM utilizes a model pool of weighted candidate models, adapted online using Bayesian formalism to capture possible temporal evolutions of the data. This review comprehensively describes BDEMM from five perspectives: its theoretical foundations, algorithms, practical applications, connections to other research, and strengths, limitations, and potential future directions.