Non-stationary Time Series Data Research Articles

Short-term load forecasting of mixed industrial users in distribution networks using DARTS-LSTM method

Abstract Load forecasting has perennially stood as a fundamental pillar within the power industry, with precision in prognostication constituting a paramount necessity for critical functions including grid management, optimization of energy storage, and response to demand fluctuations. In the present study, we introduce a comprehensive global modeling prediction framework aimed at forecasting large-scale power demand within time series data, alongside the development of a novel short-term power load forecasting model. By integrating all time series data pertaining to the same regression task and employing a unified univariate prediction function across the entire time series dataset, we efficaciously forecast large-scale heterogeneous loads aggregated at various levels within distribution networks. The proposed framework leverages the cutting-edge DARTS (Differentiable Architecture Search) deep learning framework for implementation. Through comprehensive experimentation on real-world data, our model framework demonstrates superior performance in terms of overall prediction accuracy, scalability, and robustness in handling missing and non-stationary time series data.

IMPLEMENTATION OF VECTOR AUTOREGRESSIVE (VAR) AND VECTOR ERROR CORRECTION MODEL (VECM) METHOD IN PNEUMONIA PATIENTS WITH WEATHER ELEMENTS IN PANGKALPINANG CITY

The news about Covid-19 is no longer as scary as in previous years. As COVID-19 cases decrease, health protocols are becoming more relaxed, making it easier for the virus to spread. Besides COVID-19, ARI is one of Indonesia's leading causes of death for children under five. Around 20-40% of hospital admissions are children due to ARI, with around 1.6 million deaths due to pneumonia alone in children under five per year. Currently, ARI dominates the diseases most suffered by the people of Bangka Belitung. Based on this, using the VAR and VECM method to analyze pneumonia sufferers in toddlers regarding weather elements in the Pangkalpinang City. The VAR model has a simpler structure with a minimal number of variables where all the variables are endogenous, with the independent variable being the lag. Meanwhile, VECM can be used to model cointegrated and non-stationary time series data. The data used in this research is the number of monthly cases of toddlers suffering from pneumonia and data on climate conditions, namely rainfall, air temperature, air humidity and duration of sunlight during 2019-2021 in Pangkalpinang City. The results of the Granger Causality test show that the pneumonia variables regarding rainfall, temperature, duration of sunlight and humidity only have a one-way causality pattern. The VAR estimation results show that weather elements (rainfall, temperature and duration of sunlight) do not significantly affect pneumonia in the short term. Meanwhile, the VECM estimation results show that in the long-term pattern, humidity variables affect pneumonia. For this reason, it is recommended that the relevant agencies carry out outreach to the public, especially to pneumonia sufferers, to avoid damp weather. Because the lower the humidity value, the greater the potential for pneumonia in Pangkalpinang City, Bangka Belitung Islands Province.

A Bayesian non-stationary heteroskedastic time series model for multivariate critical care data.

We propose a multivariate GARCH model for non-stationary health time series by modifying the observation-level variance of the standard state space model. The proposed model provides an intuitive and novel way of dealing with heteroskedastic data using the conditional nature of state-space models. We follow the Bayesian paradigm to perform the inference procedure. In particular, we use Markov chain Monte Carlo methods to obtain samples from the resultant posterior distribution. We use the forward filtering backward sampling algorithm to efficiently obtain samples from the posterior distribution of the latent state. The proposed model also handles missing data in a fully Bayesian fashion. We validate our model on synthetic data and analyze a data set obtained from an intensive care unit in a Montreal hospital and the MIMIC dataset. We further show that our proposed models offer better performance, in terms of WAIC than standard state space models. The proposed model provides a new way to model multivariate heteroskedastic non-stationary time series data. Model comparison can then be easily performed using the WAIC.

Time-frequency co-movements between commodities and global economic policy uncertainty across different crises

Commodity futures constitute an attractive asset class for portfolio managers. Propelled by their low correlation with other assets, commodities begin gaining popularity among investors, as they allow to capture diversification benefits. This comprehensive study examines the time and frequency spillovers between the Economic Policy Uncertainty [1] and a broad set of commodities encompassing ferrous, non-ferrous, and precious metals, food, and energy commodities over a period from December 1997 to April 2022, which includes various political, economic and health crises.The novelty of this research lies in its extensive temporal and categorical coverage, providing an understanding of how different types of commodities respond to various crises. Furthermore, our study breaks new ground by employing wavelet analysis to gain detailed insights in both time and frequency domains in the financial time series of interest, providing a deeper understanding of the co-movements and lead-lag relationships. Specifically, we introduce the Cross Wavelet Transform (XWT) and Wavelet Coherence (WTC) analysis.Our findings demonstrate that not all crises uniformly impact commodities. Notably, during the global financial crisis and the COVID-19 pandemic, co-movements between commodities became significantly stronger. These results highlight the heterogeneity within the commodity asset class, where individual commodities exhibit diverse underlying dynamics. Importantly, the proposed methodology facilitates the extraction of robust results even when dealing with nonlinearities and nonstationary time series data. Consequently, our work offers valuable insights for policymakers (including regulatory bodies), investors, and fund managers.

Ensemble Conformalized Quantile Regression for Probabilistic Time Series Forecasting.

This article presents a novel probabilistic forecasting method called ensemble conformalized quantile regression (EnCQR). EnCQR constructs distribution-free and approximately marginally valid prediction intervals (PIs), which are suitable for nonstationary and heteroscedastic time series data. EnCQR can be applied on top of a generic forecasting model, including deep learning architectures. EnCQR exploits a bootstrap ensemble estimator, which enables the use of conformal predictors for time series by removing the requirement of data exchangeability. The ensemble learners are implemented as generic machine learning algorithms performing quantile regression (QR), which allow the length of the PIs to adapt to local variability in the data. In the experiments, we predict time series characterized by a different amount of heteroscedasticity. The results demonstrate that EnCQR outperforms models based only on QR or conformal prediction (CP), and it provides sharper, more informative, and valid PIs.

Economic determinants of environmental degradation: A time series analysis of Saudi Arabian economy

Environmental degradation is posing several challenges worldwide and hence Saudi Arabia (KSA) is no exception. This paper therefore focuses on the economy of KSA to explore the main determinants of environmental degradation. The analysis of the study is based on the time-series data covering the period 1990–2022. The “Autoregressive Distributed Lag Modeling (ARDL)” is used for the estimation purpose which is recently developed in the literature for handling non-stationary time series data. For testing the direction of relationship, the study utilizes the causality testing procedure. The results indicated that energy consumption, GDP per capita and foreign direct investment have degraded the environmental quality of KSA during the study period. On the other hand, financial development and natural resource sector have improved the quality of the environment. Furthermore, trade openness appeared to be an irrelevant factor in determining the quality of the environment due to its insignificant coefficient. Finally, the causality testing showed several one-way and one two-way casual relationships among the variables used in the study. Based on the results, the current study presents several important policy implications for the policymakers of KSA. We hope that the current study will add to the literature on the economy of KSA enormously.

Study on Prediction of Zinc Grade by Transformer Model with De-Stationary Mechanism

At present, in the mineral flotation process, flotation data are easily influenced by various factors, resulting in non-stationary time series data, which lead to overfitting of prediction models, ultimately severely affecting the accuracy of grade prediction. Thus, this study proposes a de-stationary attention mechanism based on the transformer model (DST) to learn non-stationary information in raw mineral data sequences. First, normalization processing is performed on matched flotation data and mineral grade values, to make the data sequences stationary, thereby enhancing model prediction capabilities. Then, the proposed de-stationary attention mechanism is employed to learn the temporal dependencies of mineral flotation data in the transformed vanilla transformer model, i.e., non-stationary information in the mineral data sequences. Lastly, de-normalization processing is conducted to maintain the mineral prediction results within the same scale as the original data. Compared with existing models such as RNN, LSTM, transformer, Enc-Dec (RNN), and STS-D, the DST model reduced the RMSE by 20.8%, 20.8%, 62.8%, 20.5%, and 49.1%, respectively.

Does Gender Kuznets Curve Exist in South Asian Countries? Role of Gender Equality and Economic Development

This study aims to determine the relationship between gender equality and economic growth in major South Asian countries. This study suggests checking the gender Kuznets curve or whether the data support a linear, quadratic, or cubic gender Kuznets curve for major South Asian countries. We used time series data and covered the period from 1980 to 2019. We applied the Ng-Perron unit root test to check for non-stationary time series data. After the integration order is established, the autoregressive distributive lag (ARDL) model is used in three steps. The ARDL bound testing approach of covariance shows that Sri Lanka has an S-shaped Gender Cognition Curve (GKC), India has a Z-shaped GKC, Pakistan has an S-shape, and Bangladesh has an S-shape. is the -shaped GKC association. Periods of countries were considered. We also conclude that gender equality is not a direct result of development. Consequently, politicians with gender equality policies should subsidize women's employment in times of financial hardship.

Enhancing the predictive performance of non-stationary time series data through various transformations

Enhancing the predictive performance of non-stationary time series data through various transformations

Analisis Data Time Series Menggunakan Model Kernel: Pemodelan Data Harga Saham MDKA

<p>Classic time series data analysis techniques, such as autoregressive, model stationary data in which the values of prior observations influence the current observations through a process known as linear regression. There are several requirements for error assumptions in autoregressive, including independence, normal distribution with a zero mean and constant variance. It is frequently discovered that these assumptions are challenging to verify when modelling real data. Kernel time series regression is an alternative model that does not require error assumptions. Non-stationary time series data can be effectively modelled using the kernel time series method. Time series data that isn't yet stationary is made stationary first, then the data is modified by forming the current stationary time series data as the response variable and the previous period data as the predictor variable. Next, regression kernel modelling is carried out while applying kernel weight function and determining the optimal bandwidth. For development of science, the optimal bandwidth can be achieved by minimizing the MSE, CV, GCV, or UBR values. It is possible to use R<sup>2</sup> or MAPE as the kernel time series regression model's goodness metric. A strong model is generated while modelling MDKA stock price data using kernel regression utilizing the Gaussian kernel function and optimal bandwidth selection using GCV since R<sup>2</sup> is 0.9828372 more than 0.67 and MAPE is 1.985681% under 10%.</p><p><strong>Keywords</strong><strong>: </strong>3 time series; kernel regression; GCV; MDKA stock price.</p>

Distribution network planning method: Integration of a recurrent neural network model for the prediction of scenarios

The integration of new types of consumers and prosumers into distribution networks presents significant challenges for network planners, especially given the uncertainties of future expansions. This paper introduces a method for distribution network planning that integrates a Long-Short Term Memory (LSTM) model with a confidence interval threshold for long-term scenario predictions. The proposed forecasting model considers datasets collected from monitoring systems which include aggregated demand and self-consumption from photovoltaic sources. The use of the LSTM model enables a more accurate prediction of expansions, as it captures nonlinear patterns in time series data while taking into account the inherent characteristics of non-stationary time series data. The proposed method was tested on an existing radial medium voltage distribution network in Spain, taking into account the operational thermal limits for lines and substation time series measurements. The proposed planning approach also considers asset costs, active planning solutions, and time-series load flow analysis. The results obtained indicate that the use of time-based forecasts from aggregated generation and demand is a more realistic solution for flexible planning solutions when they are compared to traditional strategies.

Causal Discovery in Financial Markets: A Framework for Nonstationary Time-Series Data

Causal Discovery in Financial Markets: A Framework for Nonstationary Time-Series Data

A novel hybrid approach to mooring tension prediction for semi-submersible offshore platforms

The accuracy of mooring tension prediction significantly affects the safety of semi-submersible offshore platform operations and the efficiency of production planning. Nevertheless, traditional single prediction models have difficulty accurately forecasting for complex measured mooring tension data. This work provides a hybrid method for predicting mooring tension on semi-submersible maritime platforms based on VMD, error correction, and the convolutional neural network–long short-term memory (CNN-LSTM) and convolutional neural network–bidirectional long short-term memory (CNN-BiLSTM) models. The proposed hybrid prediction model was trained, validated, and tested using monitored mooring tension data acquired from the “Deepsea One” semi-submersible ocean platform in the South China Sea under different orientations and sea conditions. The results showed that the proposed hybrid prediction model for mooring tension on semi-submersible offshore platforms had lower values of the root mean square error, mean absolute error, and mean absolute percentage error and higher values of the coefficient of determination (R2) than almost all of the other comparison models when predicting complex time series data of the actual monitored mooring tension. This indicated that the proposed hybrid prediction model had better precision and stability than other models. Furthermore, this method can be used to anticipate nonlinear, nonstationary time series data in different fields of maritime engineering.

Anomaly Detection in Airliner Centrifugal Compressor Using Sensor Data during the Climb Phase

In recent years, aircraft have been able to quickly acquire vast and diverse sensor data, leading to the expansion of predictive maintenance applications. Centrifugal compressors are crucial to aircraft air conditioning systems, which has a high need for anomaly detection due to the impact of failures. However, due to non-stationary behavior, there is a challenge in anomaly detection of the air conditioning system. In this study, we propose a method of detecting anomalies by comparison of actual and predicted behavior of centrifugal compressors for non-stationary time-series data. Multiple failure cases confirmed that bearing deterioration results in changes in behavior.

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.

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.

Tsunami waveform forecasting at cooling water intakes of nuclear reactors with deep learning model

The Fukushima nuclear disaster highlights the importance of accurate and fast predictions of tsunami hazard to critical coastal infrastructure to devise mitigation strategies in both long-term and real-time events. Recently, deep learning models allowed us to make accurate and rapid forecasts on high dimensional, non-linear, and non-stationary time series data such as that associated with tsunami waveforms. Thus, this study uses a one-dimensional convolutional neural network (CNN) model to predict waveforms at cooling water intakes of nuclear power plant at Uljin in South Korea. The site is particularly vulnerable to tsunamis originating from the west coast of Japan. Data for the CNN model are generated by numerical simulation of 1107 cases of tsunami propagation initiating from fault locations. The time series data for waveforms were predicted at 13 virtual gauges located in the nearshore region of the study area, 10 of which were classified as observation points and 3 gauges situated at the cooling water intakes were categorized as target locations. The performance assessment of the model's forecasts showed excellent results with rapid predictions. The study highlights two main points: (i) deep learning models can be based on sparse waveform in situ data (such as that recorded by deep-ocean assessment and reporting of tsunamis or any locally operating monitoring stations for ocean waves) or numerically simulated data at only a few points along the dominant wave propagation direction, and (ii) deep learning models are fully capable of accurate and fast predictions of complex geo-hazards that prompt rapid emergency response to coordinate mitigation efforts.

Comparison of ARIMA and LSTM in Predicting Structural Deformation of Tunnels during Operation Period

Accurately predicting the structural deformation trend of tunnels during operation is significant to improve the scientificity of tunnel safety maintenance. With the development of data science, structural deformation prediction methods based on time-series data have attracted attention. Auto Regressive Integrated Moving Average model (ARIMA) is a classical statistical analysis model, which is suitable for processing non-stationary time-series data. Long- and Short-Term Memory (LSTM) is a special cyclic neural network that can learn long-term dependent information in time series. Both are widely used in the field of temporal prediction. In view of the lack of time-series prediction in the tunnel deformation field, the body of this paper uses historical data of the Xinjian Road and the Dalian Road tunnel in Shanghai to propose a new way of modeling based on single points and road sections. ARIMA and LSTM models are applied in comprehensive experiments, and the results show that: (1) Both LSTM and ARIMA models have great performance for settlement and convergence deformation. (2) The overall robustness of ARIMA is better than that of LSTM, and it is more adaptable to the datasets. (3) The model prediction performance is closely related to the data quality. ARIMA has more stable performance under the lack of data volume, while LSTM has better performance with high-quality data and higher upper limit.

Non-Gaussian feature distribution forecasting based on ConvLSTM neural network and its application to robust machine condition prognosis

The prognosis of a machine condition becomes a hot topic nowadays, as the condition monitoring installations provide a massive amount of Health Index (HI) data that could be used for machine remaining lifetime prognosis. However, existing methodologies might not be effective since in many cases the real HI datasets exhibit non-Gaussian characteristics. Thus, to improve efficiency, there is a need to introduce novel approaches which take into account the possible non-Gaussian distribution of HI data. In the proposed methodology, several innovative components are considered to form an efficient solution for the HI time series prediction. As HI is a mixture of trend and random non-Gaussian, non-homogeneous noise, we propose to forecast the HI distribution rather than the direct HI value. The Skewed Generalized t (SGT) distribution is considered as the general non-Gaussian model. Moreover, the combination of convolutional neural network (CNN) and long short-term memory (LSTM) are used to predict SGT distribution parameters. By incorporating the standardization module and the modified activation function alongside a custom time series standardization method, the architecture of the ConvLSTM neural network is created to be appropriate for non-stationary time series data with non-Gaussian behavior. Finally, a pre-training of the model has been proposed, which improves the efficiency of the designed procedure, as usually the amount of HI data is limited and insufficient to reliably train an artificial intelligence (AI) system. The proposed solution is shown to be robust and more resilient to outliers than the classical Gaussian-based approach. Using simulated and real HI data (known as a benchmark), we may conclude that the superiority of our method increases with the increasing non-Gaussianity level of the analyzed time series.

Koopman-inspired approach for identification of exogenous anomalies in nonstationary time-series data

In many scenarios, it is necessary to monitor a complex system via a time-series of observations and determine when anomalous exogenous events have occurred so that relevant actions can be taken. Determining whether current observations are abnormal is challenging. It requires learning an extrapolative probabilistic model of the dynamics from historical data, and using a limited number of current observations to make a classification. We leverage recent advances in long-term probabilistic forecasting, namely Deep Probabilistic Koopman, to build a general method for classifying anomalies in multi-dimensional time-series data. We also show how to utilize models with domain knowledge of the dynamics to reduce type I and type II error. We demonstrate our proposed method on the important real-world task of global atmospheric pollution monitoring, integrating it with NASA’s Global Earth Observing System Model. The system successfully detects localized anomalies in air quality due to events such as COVID-19 lockdowns and wildfires.