Nonstationary Time Series Research Articles

Assessment of the Contribution of Scientific and Technological Progress to the Real GDP of Russia

The paper discusses the assessment of the contribution of scientific and technological progress to the real gross domestic product (GDP) of Russia. The instrument of this assessment is the production function of the national economy. The paper presents two variants of the production function of the Russian economy, which have successfully passed all the diagnostic procedures adopted in econometrics. In the first variant, the index of scientific and technological progress (STP) is included in the set of explanatory factors such as the level of fixed capital, the amount of live labor, the price of oil, the indicator of Russia's default, the Global Financial Crisis and sanctions of Western countries. In the second variant of the production function, there is no NTP index. The scheme of construction of the production function consists of two stages. At the first stage of the scheme, statistical models of the production function are evaluated with mandatory testing of the hypothesis of the cointegration of non-stationary time series of logarithms of Russia's GDP levels, fixed capital and living labor levels and oil price levels. At the second stage of the scheme, the stability of estimates of the production function calculated from different training samples was investigated, and the accuracy of ex-post forecasting was estimated. At the second stage of the production function construction scheme, the model with the NTP index showed higher accuracy of post-factum forecasting. This circumstance, combined with the result of testing the statistical hypothesis about the presence of scientific and technological progress in the Russian economy, made it possible to assess its contribution to real GDP: other things being equal, scientific and technological progress increases the annual real GDP of Russia by about 0,6%.

Novel hybrid multi-head self-attention and multifractal algorithm for non-stationary time series prediction

Traditional time series prediction methods have shown their outstanding capabilities in time series prediction. However, due to essential differences in volatility characteristics among diverse types of non-stationary multivariate time series (NSMTS), it is difficult for traditional methods to maintain robust prediction performance. This study proposes a novel dynamic recurrent neural network to achieve stable and robust prediction performance. First, a multifractal gated recurrent unit (MF-GRU) based on the multifractal method is proposed to extract volatility characteristics. Meanwhile, to strengthen the parameters of the historical hidden layer state that has a more significant impact on the output, a self-attention mechanism is introduced into the MF-GRU, leading to a multifractal gated recurrent unit multi-head self-attention model. The efficiency of the proposed model was verified on public datasets. The experimental results show that the proposed model outperforms the traditional methods, such as long short-term memory (LSTM), the gated recurrent unit (GRU), and the minimal gated unit (MGU). etc.

The Research on Risk Distribution and Evolution of Deep Foundation Pit Construction Adjacent to Existing Tunnels Based on Complex Network

The construction of deep foundation pits adjacent to existing subway tunnels faces enormous challenges, and once a safety accident occurs, there are often mass injuries that cause substantial economic losses. However, there are many shortcomings and defects in the traditional methods of assessing the safety of the pit itself and the existing tunnel in the construction of the deep foundation pit adjacent to existing tunnels. This study establishes an optimized complex network-based dynamic risk assessment model to dynamically assess the overall risk of deep foundation pits in adjacent existing tunnels systematically, solving the challenges of inaccurate risk assessment and inaccurate description of correlations between nonstationary time series data. In this study, we first divide the monitoring data into time windows and describe the correlation between nonstationary time-series monitoring data within each window based on the MF-DCCA method and the threshold method, and establish the adjacency matrix to prepare for the establishment of an optimized complex network model. Secondly, based on the adjacency matrix, a complex network model under different time windows is constructed, and risk assessment indexes are established through the topological parameters of the complex network model to explore the evolution of risk in time and space, so as to realize the risk distribution and quantitative evolution assessment of the system which is deep foundation pit adjacent to existing subway tunnels. Finally, the proposed method is tested by taking the Nanning underground comprehensive utilization project as an example. The results show that this method can quantify the risk of the construction of deep foundation pits adjacent to existing tunnels more effectively than the traditional method to describe the evolution law better. It has important guiding significance for strengthening the safety risk monitoring and safety management of the construction system of deep foundation pits adjacent to existing tunnels.

Empirical mode decomposition using deep learning model for financial market forecasting.

Financial market forecasting is an essential component of financial systems; however, predicting financial market trends is a challenging job due to noisy and non-stationary information. Deep learning is renowned for bringing out excellent abstract features from the huge volume of raw data without depending on prior knowledge, which is potentially fascinating in forecasting financial transactions. This article aims to propose a deep learning model that autonomously mines the statistical rules of data and guides the financial market transactions based on empirical mode decomposition (EMD) with back-propagation neural networks (BPNN). Through the characteristic time scale of data, the intrinsic wave pattern was obtained and then decomposed. Financial market transaction data were analyzed, optimized using PSO, and predicted. Combining the nonlinear and non-stationary financial time series can improve prediction accuracy. The predictive model of deep learning, based on the analysis of the massive financial trading data, can forecast the future trend of financial market price, forming a trading signal when particular confidence is satisfied. The empirical results show that the EMD-based deep learning model has an excellent predicting performance.

Adaptive Broad Echo State Network for Nonstationary Time Series Forecasting

Time series forecasting provides a vital basis for the control and management of various systems. The time series data in the real world are usually strongly nonstationary and nonlinear, which increases the difficulty of reliable forecasting. To fully utilize the learning capability of machine learning in time series forecasting, an adaptive broad echo state network (ABESN) is proposed in this paper. Firstly, the broad learning system (BLS) is used as a framework, and the reservoir pools in the echo state network (ESN) are introduced to form the broad echo state network (BESN). Secondly, for the problem of information redundancy in the reservoir structure in BESN, an adaptive optimization algorithm for the BESN structure based on the pruning algorithm is proposed. Thirdly, an adaptive optimization algorithm of hyperparameters based on the nonstationary test index is proposed. In brief, the structure and hyperparameter optimization algorithms are studied to form the ABESN based on the proposed BESN model in this paper. The ABESN is applied to the data forecasting of air humidity and electric load. The experiments show that the proposed ABESN has a better learning ability for nonstationary time series data and can achieve higher forecasting accuracy.

MEEMD Decomposition-Prediction-Reconstruction Model of Precipitation Time Series.

To address the problem of low prediction accuracy of precipitation time series data, an improved overall mean empirical modal decomposition–prediction–reconstruction model (MDPRM) is constructed in this paper. First, the non-stationary precipitation time series are decomposed into multiple decomposition terms by the improved overall mean empirical modal decomposition (MEEMD). Then, a particle swarm optimization support vector machine (PSO-SVM) and convolutional neural network (CNN) and recurrent neural network (RNN) models are used to make predictions according to the characteristics of different decomposition terms. Finally, the prediction results of each decomposition term are superimposed and reconstructed to form the final prediction results. In addition, the application is carried out with the summer precipitation in the Wujiang River basin of Guizhou Province from 1961 to 2018, using the first 38 years of data to train MDPRM and the last 20 years of data to test MDPRM, and comparing with a feedback neural network (BP), a support vector machine (SVM), a particle swarm optimization support vector machine (PSO-SVM), a convolutional neural network (CNN), and a recurrent neural network (RNN), etc. The results show that the mean relative error (MAPE) of the proposed MDPRM is reduced from 0.31 to 0.09, the root mean square error (RMSE) is reduced from 0.56 to 0.30, and the consistency index (α) is significantly improved from 0.33 to 0.86, which has a higher prediction accuracy. Finally, the trained MDPRM predicts the average summer precipitation in the Wujiang River basin from 2019 to 2028 to be 466.42 mm, the minimum precipitation in 2020 to be 440.94 mm, and the maximum precipitation in 2024 to be 497.94 mm. Based on the prediction results, the agricultural drought level is evaluated using the Z index, which indicates that the summer is normal in the 10-year period. The study provides technical support for the effective guidance of regional water resources’ allocation and scheduling and drought mitigation.

An improved deep echo state network inspired by tissue-like P system forecasting for non-stationary time series

As a recurrent neural network, ESN has attracted wide attention because of its simple training process and unique reservoir structure, and has been applied to time series prediction and other fields. However, ESN also has some shortcomings, such as the optimization of reservoir and collinearity. Many researchers try to optimize the structure and performance of deep ESN by constructing deep ESN. However, with the increase of the number of network layers, the problem of low computing efficiency also follows. In this paper, we combined membrane computing and neural network to build an improved deep echo state network inspired by tissue-like P system. Through analysis and comparison with other classical models, we found that the model proposed in this paper has achieved great success both in predicting accuracy and operation efficiency.

Co-integration theory-based cluster time-varying load optimization control model of regional integrated energy system

The industrial park is an area zoned and planned for the purpose of industrial development. Although it contributes to economic growth and social development, it is also the main area of carbon emission. However, the industrial park always faces the problems of imbalances between supply and demand, which have a huge impact on the goal of energy saving and consumption reduction. Therefore, by studying the source-load interaction problem of the regional integrated energy system, this paper conducts energy supply and demand side management, which achieve lean control of regional loads. First of all, based on the time-varying characteristics of the distributed load in the region, cluster the loads and analyze the supply and demand trends for clusters. After that, considering the production process parameters, decentralized autonomous control is implemented for the cluster time-varying load. Lastly, the validity and accuracy of the model are verified by applying the model to the oilfield production area and the offshore oilfield platform system. The results show that the source-load co-integration model achieves the supply and demand matching in regional integrated energy system. Solve the problem that non-stationary time series may create spurious regression. In addition, it can be seen from the simulation results of the examples, the co-integration-based cluster control strategy improves the energy utilization by nearly 40%, which helps to achieve the goal of regionally efficient and stable production.

Are Term Premiums Predictable in Central European Countries? The Forward Rates Agreements (FRA) Application

ABSTRACT The aim of this paper is to decide whether or not term premiums appear and thus are predictable in Central European countries in the data sample of forward rate agreement interest rates and corresponding spot interest rates. Term premiums theoretically are explained thanks to the applications of the efficient market hypothesis theory, the expectations theory, and the liquidity preferences theory. Empirically, we used cointegration techniques for nonstationary time series, mainly using the cointegration method (simple and even for panel data) and the vector error correction model. We used data samples of Central European countries (the Czech Republic, Hungary, Poland) and also of the United Kingdom. We found that the best future estimate of term premiums is its current value. It does not refer in the same way to the market efficiency hypothesis (EMH) or theexpectations hypothesis (EH).

Stability Analysis of Bitcoin using Recurrence Quantification Analysis

Cryptocurrencies are new kinds of electronic currencies based on communication technologies. These currencies have attracted the attention of investors. However, cryptocurrencies are very volatile and unpredictable. For investors, it is very difficult to make investment decisions in cryptocurrency market. Therefore, revealing changes in the dynamics of cryptocurrencies are valuable for investors. Bitcoin is the most popular and representative cryptocurrency in cryptocurrency market. In this study how dynamical properties of Bitcoin changed through time is analyzed with recurrence quantification analysis (RQA). RQA is a pattern recognition-based time series analysis method that reveals dynamics of the time series by calculating some metrics called RQA measures. This method has been successfully applied to nonlinear, nonstationary, short and chaotic time series and does not assume a statistical model. RQA can reveal important properties of time series data such as determinism, laminarity, stability, randomness, regularity and complexity. By using sliding window RQA we show that in 2021 RQA measures for Bitcoin prices collapse and Bitcoin becomes more unpredictable, more random, more unstable, more irregular and less complex. Therefore, dynamics and stability of the Bitcoin prices significantly changed in 2021.

Identification of the differencing operator of a non-stationary time series via testing for zeroes in the spectral density

A nonparametric procedure for identifying the differencing operator of a non-stationary time series is presented and tested. Any proposed differencing operator is first applied to the time series, and the spectral density is tested for zeroes corresponding to the polynomial roots of the operator. A nonparametric tapered spectral density estimator is used, and the subsampling methodology is applied to obtain critical values. Simulations explore the effectiveness of the procedure under a variety of scenarios involving non-stationary processes.

ESTIMATION AND INFERENCE WITH NEAR UNIT ROOTS

New methods are developed for identifying, estimating, and performing inference with nonstationary time series that have autoregressive roots near unity. The approach subsumes unit-root (UR), local unit-root (LUR), mildly integrated (MI), and mildly explosive (ME) specifications in the new model formulation. It is shown how a new parameterization involving a localizing rate sequence that characterizes departures from unity can be consistently estimated in all cases. Simple pivotal limit distributions that enable valid inference about the form and degree of nonstationarity apply for MI and ME specifications and new limit theory holds in UR and LUR cases. Normalizing and variance stabilizing properties of the new parameterization are explored. Simulations are reported that reveal some of the advantages of this alternative formulation of nonstationary time series. A housing market application of the methods is conducted that distinguishes the differing forms of house price behavior in Australian state capital cities over the past decade.

Identification of causal relationships in non-stationary time series with an information measure: Evidence for simulated and financial data

Identification of causal relationships in non-stationary time series with an information measure: Evidence for simulated and financial data

Temporal Theil scaling in diffusive trajectory time series.

Temporal fluctuation scaling (TFS) is a power-law relation between the variance (Ξ) and the mean (Υ) which is present in cumulative time series. Taking into account that Theil index (T) can be assumed as a measure of dispersion and considering diffusive trajectory time series, we find a power-law relation between T and Υ of the form T∼(1-cΥ)^{β}, which we call temporal Theil scaling (TTS). Specifically, by analyzing data of volatility and absolute log-return for 24 nonstationary time series of financial markets, meteorology, and COVID-19 spread, we find that TTS is present in diffusive trajectory time series, while TFS is not present. Furthermore, we show that the power-law relation of TTS has a form that is similar to the relation between order parameter and temperature, which is found in the Ginzburg-Landau theory when the nontrivial critical points of an energy functional F_{η,δ} containing arbitrary powers η and δ of the order parameter are calculated.

Construction of Inflation Forecasting Model Based on Ensemble Empirical Mode Decomposition and Bayesian Model

The high explanatory power of the first-order lag term of inflation in the inflation explanatory factor is that, on the one hand, the calculation of annual inflation indicators makes the inflation values of adjacent months cover the high correlation caused by the common price increase, and on the other hand, it also shows that people’s perception of inflation is high. Some adaptability is expected. Although there are many Bayesian models available, due to the limitation of high-dimensional characteristics of the economy, most of the current inflation forecasting researches focus on a variety of generalized naive Bayesian models. By summarizing and analyzing the structural characteristics, learning methods, and classification principles of different Bayesian models, this paper finds out the important factors that affect the performance of the models and provides a theoretical basis for further improving the performance of Bayesian inflation forecasting. In this paper, the empirical mode decomposition method is introduced into inflation forecasting, and EEMD has obvious advantages in dealing with nonstationary and nonlinear time series and can decompose the signal according to the time scale characteristics of the data itself. Decompose the original time series step by step to generate eigenmode functions with different time scales. It is divided into high-frequency sequence and low-frequency sequence. Use rolling method and iterative method to construct subsamples for the sample data in this sample interval, forecast the inflation rate of each subsample interval in the next 12 months, and then compare the predicted value with the actual value to obtain a certain constructive conclusion. The predicted value is relatively close to the real value, which has theoretical and practical significance, and the predicted results obtained have no obvious regularity, but the root mean square error can be kept within 60%. By comparing the predicted value and the actual value, it can be seen that the prediction effect of the EEMD model is better.

Empirical adaptive wavelet decomposition (EAWD): an adaptive decomposition for the variability analysis of observation time series in atmospheric science

Abstract. Most observational data sequences in geophysics can be interpreted as resulting from the interaction of several physical processes at several timescales and space scales. In consequence, measurement time series often have characteristics of non-linearity and non-stationarity and thereby exhibit strong fluctuations at different timescales. The application of decomposition methods is an important step in the analysis of time series variability, allowing patterns and behaviour to be extracted as components providing insight into the mechanisms producing the time series. This study introduces empirical adaptive wavelet decomposition (EAWD), a new adaptive method for decomposing non-linear and non-stationary time series into multiple empirical modes with non-overlapping spectral contents. The method takes its origin from the coupling of two widely used decomposition techniques: empirical mode decomposition (EMD) and empirical wavelet transformation (EWT). It thus combines the advantages of both methods and can be interpreted as an optimization of EMD. Here, through experimental time series applications, EAWD is shown to accurately retrieve different physically meaningful components concealed in the original signal.

Forecasting Crude Oil Consumption in Poland Based on LSTM Recurrent Neural Network

Primary fuels, i.e., crude oil, natural gas, and power coal, dominate the total global demand for primary energy. Among them, crude oil plays a particularly important role due to the universality of applications and the practical lack of substitutes in transport. Crude oil is also one of the main sources of primary energy in Poland and accounts for around 30% of the energy consumed. Poland covers only 3% of its needs from domestic deposits. The rest is imported from Russia, Saudi Arabia, Nigeria, Great Britain, Kazakhstan, and Norway. Due to such a high import of raw material, Poland must anticipate future demand. On the one hand, this article aims to analyze the current (2020) and future (2040) crude oil consumption on the Polish market. The study analyzes the geopolitical and economic foundations of the functioning of the energy raw-materials market, the crude oil supply, the structure of Poland’s energy mix, and assumptions about the energy policy until 2040. On the other hand, conclusions from the research were used to build a model of crude oil consumption for the internal market. It has been also shown that the consumption of crude oil on the Polish market is a nonlinear phenomenon with a small set of statistical data, which makes it difficult to build an accurate model. This paper proposes a new model based on artificial neural networks that includes long-term memory (LSTM). The accuracy of the constructed model was assessed using the MSE, Theil, and Janus coefficients. The results show that LSTM models can be used to forecast crude oil consumption, and they cope with the nonstationary and nonlinear time series. Many important contemporary problems posed in the field of energy economy are also discussed, and it is proposed to solve them with the use of modern machine-learning tools.

Reinforcement Learning Based Dynamic Model Combination for Time Series Forecasting

Time series data appears in many real-world fields such as energy, transportation, communication systems. Accurate modelling and forecasting of time series data can be of significant importance to improve the efficiency of these systems. Extensive research efforts have been taken for time series problems. Different types of approaches, including both statistical-based methods and machine learning-based methods, have been investigated. Among these methods, ensemble learning has shown to be effective and robust. However, it is still an open question that how we should determine weights for base models in the ensemble. Sub-optimal weights may prevent the final model from reaching its full potential. To deal with this challenge, we propose a reinforcement learning (RL) based model combination (RLMC) framework for determining model weights in an ensemble for time series forecasting tasks. By formulating model selection as a sequential decision-making problem, RLMC learns a deterministic policy to output dynamic model weights for non-stationary time series data. RLMC further leverages deep learning to learn hidden features from raw time series data to adapt fast to the changing data distribution. Extensive experiments on multiple real-world datasets have been implemented to showcase the effectiveness of the proposed method.

Exponential smoothing of dynamic series liquefaction number of corn starch mixture

The most important statistical indicators of the time series are the absolute chain and basic growth, chain and basic growth rates, growth rates, etc., which describe the current state of the process without making a forecast. The classical approach to forecasting series is based on the choice of a suitable theoretical model of the trend with unknown parameters, followed by its modeling. The applicability of the exponential smoothing method to the investigated dynamic series lies in the possibility of predicting a non-stationary time series, in which the weight of the series member decreases exponentially and practically does not have any effect on the value of the exponential average, which replaces the observed value of the series. The aim of the work was to carry out exponential smoothing of the dynamic series of the liquefaction number of the corn starch mixture. In this case, the study presents a sequence of observations of the index of liquefaction, ordered depending on the increase in the dosage of amylopectin corn starch in the corn starch mixture. The liquefaction number for corn starch mixture consisting of fine corn flour (GOST 14176) and corn amylopectin starch (GOST 32159) in the ratio: 100:0, 90:10, 80:20, 70:30, 60:40, 50:50, 40:60, 30:70, 20:80, 10:90, 0:100 were received by calculation. Exponential smoothing of the dynamic series of the liquefaction number of corn starch mixture makes it possible to obtain a reliable forecast of the dynamics of the quality indicator at the liquefaction process in the specified interval. The standard errors of the predicted values of the liquefaction number of corn starch mixture at a dosage of amylopectin corn starch in a mixture from 0% to 35.0 % inclusive are within the convergence requirements of GOST 30498 (ISO 3093) for measurement results. A stable growth in the dynamics of the number of liquefaction of corn starch mixture is provided when replacing corn flour with amylopectin corn starch in an amount of not more than 35.0 %.

Motor imagery electroencephalogram classification based on sparse spatiotemporal decomposition and channel attention

Motor imagery electroencephalogram (EEG) signals are non-stationary time series with a low signal-to-noise ratio. Therefore, the single-channel EEG analysis method is difficult to effectively describe the interaction characteristics between multi-channel signals. This paper proposed a deep learning network model based on the multi-channel attention mechanism. First, we performed time-frequency sparse decomposition on the pre-processed data, which enhanced the difference of time-frequency characteristics of EEG signals. Then we used the attention module to map the data in time and space so that the model could make full use of the data characteristics of different channels of EEG signals. Finally, the improved time-convolution network (TCN) was used for feature fusion and classification. The BCI competition IV-2a data set was used to verify the proposed algorithm. The experimental results showed that the proposed algorithm could effectively improve the classification accuracy of motor imagination EEG signals, which achieved an average accuracy of 83.03% for 9 subjects. Compared with the existing methods, the classification accuracy of EEG signals was improved. With the enhanced difference features between different motor imagery EEG data, the proposed method is important for the study of improving classifier performance.