Single Time Series Research Articles

Interval Time Series Forecasting: An Innovative Approach Transforming Interval to Single Time Series

ABSTRACTInterval Time Series are present in everyday life. An example is the opening and closing value of some stock in a market for certain time intervals. The forecasting plays an essential role in many financial organisations. The development of new mathematical tools or improving the existing ones will lead to more accurate forecasting techniques. Interval Arithmetic is a mathematical field that uses intervals by nature and algorithms that use it are involved in the solution of Interval Time Series. Another classical algorithm is VAR models. In this paper, a method that comes from the insurance sector is used to forecast Brent Oil monthly values. The innovation of what we propose is that it converts the Interval Time Series system into a single time series and can propagate the results back to each time series of the system. This way the researcher works with only one time series instead of two (or more). The forecasting algorithm is a choice of the researcher, expediting the development of forecasting (even ARIMA can be applied). We demonstrate our methodology in forecasting the Brent Oil monthly prices by applying the ANFIS algorithm.

Weeks After the Raid: The Immediate and Sustained Changes in Student Attendance Rates Following Immigration Arrests

Recent research has shown the ways in which immigration enforcement actions can affect educational outcomes for all students, regardless of their immigrant status. One consequence of particular concern is student absenteeism, a non-academic indicator used by 37 states to evaluate school success under the Every Student Succeeds Act. However, previous research has faced data limitations on the measure of immigration enforcement and relies on aggregated measures of educational outcomes. Using weekly attendance rates of a school district as well as unique data collection on immigration arrests between 2014 and 2018, this study used single and comparative interrupted time series analyses to quantify the immediate and sustained impacts of immigration arrests on student attendance. Findings suggest that incidents involving a greater number of immigration arrests correspond to immediate spikes in student absenteeism, as high as 11% points for certain student demographics. Additionally, the district’s attendance rate sustained a cumulative 2%-point decline following two incidents involving the greatest number of arrests. Implications for policymakers and educators are discussed.

Shapelet selection for time series classification

In recent times, increasing attention has been given to shapelet-based methods for time series classification. However, in the majority of current methods, similar subsequences were often selected as shapelets, thereby reducing the final interpretability of these methods. Aiming to circumvent the selection of similar subsequences as the final shapelets, a novel shapelet selection method (SSM) was proposed in this paper. Firstly, shapelet candidates were generated by SSM through time series segmentation to avoid excessive generation of similar candidates from a single time series. Secondly, all shapelet candidates were evaluated simultaneously to improve evaluation efficiency. Finally, SSM introduced a position-based filter to prevent the selection of similar sequences repeatedly. The results obtained on the UCR TSC archive demonstrated the effectiveness of the proposed method.

Residual loneliness in the Netherlands after the COVID-19 pandemic: An application of the single interrupted time series design with pre-, peri- and post-pandemic observations

ObjectivesDuring the COVID-19 pandemic, many countries implemented policies to physically separate citizens. As a consequence, an increased prevalence of loneliness was observed. This article examined whether the prevalence of loneliness in the Netherlands has returned to pre-pandemic levels after the restrictive policy was ended. We studied age differences in the course of loneliness. Study designSingle interrupted time series design. MethodsData were from the Longitudinal Internet Studies for the Social Sciences (age range 16–102 years) and the Longitudinal Aging Study Amsterdam (age range 65–101 years). Both studies included respondents sampled from the Dutch population registers. Data collected relatively soon and later after the pandemic outbreak (nine and five observations in 2020–2023, respectively) were compared to extrapolated trend data based on a long period of time before the outbreak (since 2008 and 1992, respectively). ResultsWith two exceptions, the results of the two studies including five age categories and three types of loneliness measurement instruments showed that after an increased prevalence during the pandemic, prevalence at the last observation was at or below the level of the extrapolated trend. ConclusionsIt is highly likely that the pandemic was indeed an interruption and not a fundamental trend change in loneliness. This shows individuals’ resilience and the ability to reactivate social ties after the interruptive pandemic.

Characterisation of Dansgaard–Oeschger events in palaeoclimate time series using the matrix profile method

Abstract. Palaeoclimate time series, reflecting the state of Earth's climate in the distant past, occasionally display very large and rapid shifts showing abrupt climate variability. The identification and characterisation of these abrupt transitions in palaeoclimate records is of particular interest as this allows for understanding of millennial climate variability and the identification of potential tipping points in the context of current climate change. Methods that are able to characterise these events in an objective and automatic way, in a single time series, or across two proxy records are therefore of particular interest. In our study the matrix profile approach is used to describe Dansgaard–Oeschger (DO) events, abrupt warmings detected in the Greenland ice core, and Northern Hemisphere marine and continental records. The results indicate that canonical events DO-19 and DO-20, occurring at around 72 and 76 ka, are the most similar events over the past 110 000 years. These transitions are characterised by matching transitions corresponding to events DO-1, DO-8, and DO-12. They are abrupt, resulting in a rapid shift to warmer conditions, followed by a gradual return to cold conditions. The joint analysis of the δ18O and Ca2+ time series indicates that the transition corresponding to the DO-19 event is the most similar event across the two time series.

Efficient prediction framework for large-scale nonlinear petrochemical process based on feature selection and temporal-attention LSTM: Applied to fluid catalytic cracking

Data-driven modeling plays a vital role in petrochemical industry, especially fluid catalytic cracking (FCC). However, the long operational cycles, large-scale measurements, multivariate data, and intricate temporal correlations in FCC units may lead to the problem of low prediction accuracy when only use a single time series data-driven modeling neural network such as long short-term memory (LSTM) network. To address these challenges, an effective prediction framework is proposed that integrates LSTM network with extreme gradient boosting (XGBOOST)-based feature selection and temporal-attention (TA) mechanisms. XGBOOST is applied to filter features related to the predictive variables in order to eliminate redundant variables. TA mechanisms within an LSTM network is used to capture the relevant historical time steps of the current moment. The results of our efficient prediction framework, applied to FCC process and three additional petrochemical processes, have proven to be superior to other methods.

The Bayesian reservoir model of psychological regulation.

Social and behavioral scientists are increasingly interested the dynamics of the processes they study. Despite the wide array of processes studied, a fairly narrow set of models are applied to characterize dynamics within these processes. For social and behavioral research to take the next step in modeling dynamics, a wider variety of models need to be considered. The reservoir model is one model of psychological regulation that helps expand the models available (Deboeck & Bergeman, 2013). The present article implements the Bayesian reservoir model for both single time series and multilevel data. Simulation 1 compares the performance of the original version of the reservoir model fit using structural equation modeling (Deboeck & Bergeman, 2013) to the proposed Bayesian estimation approach. Simulation 2 expands this to a multilevel data scenario and compares this to the single-level version. The Bayesian estimation approach performs substantially better than the original estimation approach and produces low-bias estimates even with time series as short as 25 observations. Combining Bayesian estimation with a multilevel modeling approach allows for relatively unbiased estimation with sample sizes as small as 15 individuals and/or with time series as short as 15 observations. Finally, a substantive example is presented that applies the Bayesian reservoir model to perceived stress, examining how the model parameters relate to psychological variables commonly expected to relate to resilience. The current expansion of the reservoir model demonstrates the benefits of leveraging the combined strengths of Bayesian estimation and multilevel modeling, with new dynamic models that have been tailored to match the process of psychological regulation. (PsycInfo Database Record (c) 2024 APA, all rights reserved).

Variational inference of single cell time series.

Time course single-cell RNA sequencing (scRNA-seq) enables researchers to probe genome-wide expression dynamics at the the single cell scale. However, when gene expression is affected jointly by time and cellular identity, analyzing such data - including conducting cell type annotation and modeling cell type-dependent dynamics - becomes challenging. To address this problem, we propose SNOW (SiNgle cell flOW map), a deep learning algorithm to deconvolve single cell time series data into time-dependent and time-independent contributions. SNOW has a number of advantages. First, it enables cell type annotation based on the time-independent dimensions. Second, it yields a probabilistic model that can be used to discriminate between biological temporal variation and batch effects contaminating individual timepoints, and provides an approach to mitigate batch effects. Finally, it is capable of projecting cells forward and backward in time, yielding time series at the individual cell level. This enables gene expression dynamics to be studied without the need for clustering or pseudobulking, which can be error prone and result in information loss. We describe our probabilistic framework in detail and demonstrate SNOW using data from three distinct time course scRNA-seq studies. Our results show that SNOW is able to construct biologically meaningful latent spaces, remove batch effects, and generate realistic time-series at the single-cell level. By way of example, we illustrate how the latter may be used to enhance the detection of cell type-specific circadian gene expression rhythms, and may be readily extended to other time-series analyses.

Modeling and Analysis of Monkeypox Outbreak Using a New Time Series Ensemble Technique

The coronavirus pandemic has raised concerns about the emergence of other viral infections, such as monkeypox, which has become a significant hazard to public health. Thus, this work proposes a novel time series ensemble technique for analyzing and forecasting the spread of monkeypox in the four highly infected countries with the monkeypox virus. This approach involved processing the first cumulative confirmed case time series to address variance stabilization, normalization, stationarity, and a nonlinear secular trend component. After that, five single time series models and three proposed ensemble models are used to estimate the filtered confirmed case time series. The accuracy of the models is evaluated using typical accuracy mean errors, graphical evaluation, and an equal forecasting accuracy statistical test. Based on the results, it is found that the proposed time series ensemble forecasting approach is an efficient and accurate way to forecast the cumulative confirmed cases for the top four countries in the world and the entire world. Using the best ensemble model, a forecast is made for the next 28 days (four weeks), which will help understand the spread of the disease and the associated risks. This information can prevent further spread and enable timely and effective treatment. Furthermore, the developed novel time series ensemble approach can be used to forecast other diseases in the future.

A hybrid reanalysis-forecast meteorological forcing data for advancing climate adaptation in agriculture

Climate variability in the growing season is well suited for testing adaptation measures. Adaptation to adverse events, such as heatwaves and droughts, increases the capacity of players in agri-food systems, not only producers but also transporters and food manufacturers, to prepare for production disruptions due to seasonal extremes and climate change. Climate impact models (e.g., crop models) can be used to develop adaptation responses. To run these models, historical records and climate forecasts need to be combined as a single daily time series. We introduce the daily 0.5° global hybrid reanalysis-forecast meteorological forcing dataset from 2010 to 2021. The dataset consists of the Japanese 55-yr Reanalysis (JRA55) and the Japan Meteorological Agency/Meteorological Research Institute Coupled Prediction System version 2 (JMA/MRI-CPS2) 5-member ensemble forecast. Both are bias-corrected using the Delta method and integrated with a baseline climatology derived from the Environmental Research and Technology Development Fund’s Strategic Research 14 Meteorological Forcing Dataset (S14FD). The dataset is called JCDS (JRA55-CPS2-Delta-S14FD) and offers a framework for monitoring and forecasting applications towards adaptation.

Research on diagnosis method of motor vibration signal based on MSCNN-LSTM

Abstract Vibration signal is often considered an important basis for diagnosing motor faults. However, the original vibration signal features a single time series that needs to be shorter. This paper introduces a fault diagnosis approach, MSCNN-LSTM, which integrates a multi-scale one-dimensional convolutional neural network with a long short-term memory network, reflecting the ongoing advancements in deep learning for fault diagnosis. Convolution kernels of varying sizes are accustomed to realizing information integration of various scales and broadening the dimensions of vibration signals. In addition, one-dimensional convolution networks effectively solve the problem of excessively long timing of original signals, and LSTM captures timing dependence for diagnosing motor faults. The experimental results indicate that MSCNN-LSTM has high accuracy in motor fault diagnosis based on vibration signals.

Earthquake source inversion by integrated fiber-optic sensing

We present an earthquake source inversion using a single time series produced by integrated fiber-optic sensing in a phase noise cancellation (PNC) system used for frequency metrology. Operating on a 123 km long fiber between Bern and Basel (Switzerland), the PNC system recorded the Mw3.9 Mulhouse earthquake that occurred on 10 September 2022 around 10 km north-west of the northern fiber end. A generalised least-squares inversion in the 4 - 13 s period band constrains the components of a double-couple moment tensor with an uncertainty that corresponds to around 0.2 moment magnitude units, nearly independent of prior information. Uncertainties for hypocenter location and original time are more variable, ranging between 4 - 20 km and 0.1 - 1 s, respectively, depending on whether injected prior information is realistic or almost absent. This work is a proof of concept that quantifies the resolvability of earthquake source properties under specific conditions using a single-channel stand-alone integrated (non-distributed) fiber-optic measurement. It thereby constitutes a step towards the integration of long-range phase-transmission fiber-optic sensors into existing seismic networks in order to fill significant seismic data gaps, especially in the oceans.

Market uncertainty and information content in complex seasonality of prices

In the context of heightened economic and financial market uncertainty, identifying and measuring uncertainty have become an important research question. This study offers a novel approach to uncover uncertainty and its sources by leveraging the complex seasonality inherent in futures prices. Our findings indicate that the temporal hierarchical forecasting method is not universally effective across 35 different commodity futures. However, further analysis reveals that this method outperforms single time series forecasting models when its manually set seasonal components align with those identified through singular spectrum analysis (SSA). The study demonstrates the efficacy of SSA in revealing complex seasonality patterns in various futures prices. Additionally, our event analysis results indicate that shifts in the seasonality patterns of commodity futures prices provide a new perspective for understanding uncertainty and exploring its origins. This research contributes to the literature by extending market uncertainty measures through the linkage with complex seasonality analysis, and offering valuable insights for risk management.

Symptoms of a feather flock together? An exploratory secondary dynamic time warp analysis of 11 single case time series of suicidal ideation and related symptoms

Suicidal ideation fluctuates over time, as does its related risk factors. Little is known about the difference or similarities of the temporal patterns. The current exploratory secondary analysis examines which risk symptoms have similar time dynamics using a mathematical algorithm called dynamic time warping (DTW). Ecological momentary assessment data was used of 11 depressed psychiatric outpatients with suicidal ideation who answered three daytime surveys at semi-random sampling points for a period of three to six months. Patients with 45 assessments or more were included. Results revealed significant inter-individual variability in symptom dynamics and clustering, with certain symptoms often clustering due to similar temporal patterns, notably feeling sad, hopelessness, feeling stuck, and worrying.The directed network analyses shed light on the temporal order, highlighting entrapment and worrying as symptoms strongly related to suicide ideation. Still, all patients also showed unique directed networks. While for some patients changes in entrapment directly preceded change in suicide ideation, the reverse temporal ordering was also found. Relatedly, within some patients, perceived burdensomeness played a pivotal role, whereas in others it was unconnected to other symptoms. The study underscores the individualized nature of symptom dynamics and challenges linear models of progression, advocating for personalized treatment strategies.

On a matrix‐valued autoregressive model

Many data sets in biology, medicine, and other biostatistical areas deal with matrix‐valued time series. The case of a single univariate time series is very well developed in the literature; and single multi‐variate series (i.e., vector time series) though less well studied have also been developed. A class of matrix time series models is introduced for dealing with situations where there are multiple sets of multi‐variate time series data. Explicit expressions for a matrix autoregressive model along with its cross‐autocorrelation functions are derived. Stationarity conditions are also provided. Least squares estimators and maximum likelihood estimators of the model parameters and their asymptotic properties are derived. Results are illustrated through simulation studies and a real data application.

A maximal overlap discrete wavelet packet transform coupled with an LSTM deep learning model for improving multilevel groundwater level forecasts

Developing precise groundwater level (GWL) forecast models is essential for the optimal usage of limited groundwater resources and sustainable planning and management of water resources. In this study, an improved forecasting accuracy for up to 3 weeks ahead of GWLs in Bangladesh was achieved by employing a coupled Long Short Term Memory (LSTM) network-based deep learning algorithm and Maximal Overlap Discrete Wavelet Packet Transform (MODWPT) data preprocessing. The coupled LSTM-MODWPT model’s performance was compared with that of the LSTM model. For both standalone LSTM and LSTM-MODWPT models, the Random Forest feature selection approach was employed to select the ideal inputs from the candidate GWL lags. In the LSTM-MODWPT model, input GWL time series were decomposed using MODWPT. The ‘Fejér-Korovkin’ mother wavelet with a filter length of 18 was used to obtain a collection of scaling coefficients and wavelets for every single input time series. Model performance was assessed using five performance indices: Root Mean Squared Error; Scatter Index; Maximum Absolute Error; Median Absolute Deviation; and an a-20 index. The LSTM-MODWPT model outperformed standalone LSTM models for all time horizons in GWL forecasting. The percentage improvements in the forecasting accuracies were 36.28%, 32.97%, and 30.77%, respectively, for 1-, 2-, and 3-weeks ahead forecasts at the observation well GT3330001. Accordingly, the coupled LSTM-MODWPT model could potentially be used to enhance multiscale GWL forecasts. This research demonstrates that the coupled LSTM-MODWPT model could generate more precise GWL forecasts at the Bangladesh study site, with potential applications in other geographic locations globally.

On the Performance of Some Estimation Methods in Models with Heteroscedasticity and Autocorrelated Disturbances (A Monte-Carlo Approach)

The proliferation of panel data studies has been greatly motivated by the availability of data and capacity for modelling the complexity of human behaviour than a single cross-section or time series data and these led to the rise of challenging methodologies for estimating the data set. It is pertinent that, in practice, panel data are bound to exhibit autocorrelation or heteroscedasticity or both. In view of the fact that the presence of heteroscedasticity and autocorrelated errors in panel data models biases the standard errors and leads to less efficient results. This study deemed it fit to search for estimator that can handle the presence of these twin problems when they co- exists in panel data. Therefore, robust inference in the presence of these problems needs to be simultaneously addressed. The Monte-Carlo simulation method was designed to investigate the finite sample properties of five estimation methods: Between Estimator (BE), Feasible Generalized Least Square (FGLS), Maximum Estimator (ME) and Modified Maximum Estimator (MME), including a new Proposed Estimator (PE) in the simulated data infected with heteroscedasticity and autocorrelated errors. The results of the root mean square error and absolute bias criteria, revealed that Proposed Estimator in the presence of these problems is asymptotically more efficient and consistent than other estimators in the class of the estimators in the study. This is experienced in all combinatorial level of autocorrelated errors in remainder error and fixed heteroscedastic individual effects. For this reason, PE has better performance among other estimators.

Adoption of a gastroenterology hospitalist model and the impact on inpatient endoscopic practice volume: a controlled interrupted time-series analysis

Background and AimsThe gastroenterology (GI) hospitalist staffing model has multiple potential benefits for the inpatient and outpatient care of GI patients. The GI hospitalist model may improve inpatient endoscopy efficiency via better provider familiarity with management of GI emergencies, hospital systems and workflow, and may also increase outpatient endoscopy capacity by decreasing the need for inpatient coverage by outpatient providers. However, the real-world impact of this model on inpatient and outpatient endoscopic volume remains uncertain. MethodsWe conducted a controlled interrupted time series analysis from September 2018 to March 2020 comparing inpatient endoscopy volume at two high-acuity hospitals within the same academic health system, one of which adopted a two-physician GI hospitalist model in July 2019. We also performed a single interrupted time series analysis of outpatient endoscopic volume of the practice employing GI hospitalists. ResultsAfter implementation of the GI hospitalist model, weekly volume of inpatient endoscopic procedures increased by 10.9 (95% CI: [0.6, 21.2]; p=0.024) compared to a hospital using traditional staffing. Outpatient endoscopic procedure volume also increased by 39.8 per week (95% CI: [-5.78, 85.44]; p=0.09), with no change in the number of physicians performing endoscopy. ConclusionsOur findings demonstrate that introduction of a GI hospitalist model increased inpatient and outpatient endoscopic volume in a large academic center.

Calcium oscillations in HEK293 cells lacking SOCE suggest the existence of a balanced regulation of IP3 production and degradation

The concentration of free cytosolic Ca2+ is a critical second messenger in almost every cell type, with the signal often being carried by the period of oscillations, or spikes, in the cytosolic Ca2+ concentration. We have previously studied how Ca2+ influx across the plasma membrane affects the period and shape of Ca2+ oscillations in HEK293 cells. However, our theoretical work was unable to explain how the shape of Ca2+ oscillations could change qualitatively, from thin spikes to broad oscillations, during the course of a single time series. Such qualitative changes in oscillation shape are a common feature of HEK293 cells in which STIM1 and 2 have been knocked out. Here, we present an extended version of our earlier model that suggests that such time-dependent qualitative changes in oscillation shape might be the result of balanced positive and negative feedback from Ca2+ to the production and degradation of inositol trisphosphate.

A Technique for Efficient Estimation of Dynamic Structural Equation Models: A Case Study

Dynamic structural equation models (DSEM) are designed for time series analysis of latent structures. Inherent to the application of DSEM is model parameter estimation, which has to be addressed in many applications by a single time series. In this context, however, the methods currently available either lack estimation quality or are computationally inefficient. Given the era of big data, the necessity for a trade-off between these properties may be detrimental to the applicability of DSEM. The paper is aimed at tackling this trade-off by proposing a novel estimator recursioning technique (ER technique) that facilitates the development of computationally efficient raw-data maximum likelihood estimation algorithms through data transformation, covariance matrix block decomposition, likelihood function reduction, and estimator recursioning steps. The ER technique is introduced by applying it to a special case of the general dynamic structural equation model that encompasses a noisy Wiener-process-type structure with input from the factor-analytic model. The resulting algorithm has been verified through a number of numerical experiments as well as implemented in a brand new R package EMLI, which is available on CRAN.