Hierarchical Time Research Articles

Improving out-of-sample forecasts of stock price indexes with forecast reconciliation and clustering

In this paper, we propose a novel approach to improving forecasts of stock market indexes by considering common stock prices as hierarchical time series, combining clustering with forecast reconciliation. We propose grouping the individual stock price series in various ways including via metadata and using unsupervised learning techniques. The proposed approach is applied to the Dow Jones Industrial Average Index and the Standard & Poor 500 Index and their component stocks, and the results obtained with different grouping approaches are compared. The results empirically demonstrate that the combined use of clustering and reconciliation improves the forecast accuracy of the stock market indexes and their constituents.

Memorizing Swin-Transformer Denoising Network for Diffusion Model

Diffusion models have garnered significant attention in the field of image generation. However, existing denoising architectures, such as U-Net, face limitations in capturing the global context, while Vision Transformers (ViTs) may struggle with local receptive fields. To address these challenges, we propose a novel Swin-Transformer-based denoising network architecture that leverages the strengths of both U-Net and ViT. Moreover, our approach integrates the k-Nearest Neighbor (kNN) based memorizing attention module into the Swin-Transformer, enabling it to effectively harness crucial contextual information from feature maps and enhance its representational capacity. Finally, we introduce an innovative hierarchical time stream embedding scheme that optimizes the incorporation of temporal cues during the denoising process. This method surpasses basic approaches like simple addition or concatenation of fixed time embeddings, facilitating a more effective fusion of temporal information. Extensive experiments conducted on four benchmark datasets demonstrate the superior performance of our proposed model compared to U-Net and ViT as denoising networks. Our model outperforms baselines on the CRC-VAL-HE-7K and CelebA datasets, achieving improved FID scores of 14.39 and 4.96, respectively, and even surpassing DiT and UViT under our experiment setting. The Memorizing Swin-Transformer architecture, coupled with the hierarchical time stream embedding, sets a new state-of-the-art in denoising diffusion models for image generation.

Forecasting hierarchical time series for foodborne disease outbreaks

Forecasting hierarchical time series for foodborne disease outbreaks

Mitigating Alarm Fatigue and Improving the Bedside Experience by Reducing Nonactionable Alarms

To assess whether conditional bedside alarm triggers can reduce the frequency of non-actionable alarms without compromising patient safety and enhance nursing and family satisfaction. Single center, quality improvement initiative in an acute care cardiac unit (ACCU) and pediatric intensive care unit (PICU). Following the 4-week pre-intervention baseline period, bedside monitors were programmed with hierarchical time delay and conditional alarm triggers. Bedside alarms were tallied for 4 weeks each in the immediate post intervention period and 2-year follow-up. The primary outcome was alarms per monitored patient day. Nurses and families were surveyed pre- and post-intervention. A total of 1509 patients contributed to 2034, 1968, and 2043 monitored patient days which were evaluated in the baseline, follow-up, and 2-year follow-up periods, respectively. The median number of alarms per monitored patient day decreased by 75% in the PICU (p<0.001) and 82% in the ACCU (p<0.001) with sustained effect at 2-year follow-up. No increase of rapid response calls, emergent transfers, or code events occurred in either unit. Nursing surveys reported an improved capacity to respond to alarms and fewer perceived non-actionable alarms. Family surveys, however, did not demonstrate improved sleep quality. Implemented changes to bedside monitor alarms decreased total alarm frequency in both the acute care cardiac unit and pediatric intensive care unit, improving the care provider experience without compromising safety.

Trial Design with Win Statistics for Multiple Time-to-Event Endpoints with Hierarchy

The conventional approach to the analysis of composite endpoints is time-to-first event analysis. However, this approach has been criticized because it ignores the differences in clinical severity and may end up emphasizing the less severe time-to-event. To overcome this limitation, win statistics (win ratio, win odds, or net benefit) have become popular in analysis of hierarchical time to event endpoints. However, design of randomized clinical trials using the win statistics is lagging behind. In this article, we derive formulas for the win statistics and probability of ties under specific assumptions that can be useful in practice. We also address two design issues: the selection of meaningful and justifiable design parameters and power calculations, when the win statistics method is the primary analysis method for multiple time-to-event endpoints for a pre-specified hierarchy. Finally, we identify patterns where the win statistics approach would have greater statistical power than time-to-first event analysis. Several examples are used to illustrate the usefulness of the formula-based power calculations.

Adaptation processes in Halomicronema hongdechloris, an example of the light-induced optimization of the photosynthetic apparatus on hierarchical time scales.

Oxygenic photosynthesis in Halomicronema hongdechloris, one of a series of cyanobacteria producing red-shifted Chl f, is adapted to varying light conditions by a range of diverse processes acting over largely different time scales. Acclimation to far-red light (FRL) above 700 nm over several days is mirrored by reversible changes in the Chl f content. In several cyanobacteria that undergo FRL photoacclimation, Chl d and Chl f are directly involved in excitation energy transfer in the antenna system, form the primary donor in photosystem I (PSI), and are also involved in electron transfer within photosystem II (PSII), most probably at the ChlD1 position, with efficient charge transfer happening with comparable kinetics to reaction centers containing Chl a. In H. hongdechloris, the formation of Chl f under FRL comes along with slow adaptive proteomic shifts like the rebuilding of the D1 complex on the time scale of days. On shorter time scales, much faster adaptation mechanisms exist involving the phycobilisomes (PBSs), which mainly contain allophycocyanin upon adaptation to FRL. Short illumination with white, blue, or red light leads to reactive oxygen species-driven mobilization of the PBSs on the time scale of seconds, in effect recoupling the PBSs with Chl f-containing PSII to re-establish efficient excitation energy transfer within minutes. In summary, H. hongdechloris reorganizes PSII to act as a molecular heat pump lifting excited states from Chl f to Chl a on the picosecond time scale in combination with a light-driven PBS reorganization acting on the time scale of seconds to minutes depending on the actual light conditions. Thus, structure-function relationships in photosynthetic energy and electron transport in H. hongdechloris including long-term adaptation processes cover 10-12 to 106 seconds, i.e., 18 orders of magnitude in time.

Forecasting the waste production hierarchical time series with correlation structure

AbstractContinuous increase in society’s prosperity causes overwhelming growth of the produced municipal solid waste. Circular economy initiatives help to solve this problem by creating closed production cycles, where the produced waste is recycled, or its energy is recovered. An embedment of such principles requires implementation of new waste management strategies. However, these novel strategies must be based on the accurate forecasts of future waste flows. Municipal solid waste production data demonstrate behavior of hierarchical time series. Among all possible approaches to hierarchical times series forecasting, this article is focused on the reconciliation of the base waste generation forecasts. The novel method, that is based on the game-theoretically optimal reconciliation of hierarchical time series, is presented. The modified approach enables to incorporate interdependencies between time series using correlation matrix and to obtain the forecasts corresponding to the unique solution of the optimization problem. The potential of the proposed abstract approach is demonstrated on the waste production data of paper, plastics (both primarily sorted by households), and mixed municipal solid waste from the Czech Republic.

MHTFPE2D: two-dimensional multi-scale hierarchical time–frequency permutation entropy for complexity measurement

MHTFPE2D: two-dimensional multi-scale hierarchical time–frequency permutation entropy for complexity measurement

Hierarchical Time Series Forecasting of Fire Spots in Brazil: A Comprehensive Approach

This study compares reconciliation techniques and base forecast methods to forecast a hierarchical time series of the number of fire spots in Brazil between 2011 and 2022. A three-level hierarchical time series was considered, comprising fire spots in Brazil, disaggregated by biome, and further disaggregated by the municipality. The autoregressive integrated moving average (ARIMA), the exponential smoothing (ETS), and the Prophet models were tested for baseline forecasts, and nine reconciliation approaches, including top-down, bottom-up, middle-out, and optimal combination methods, were considered to ensure coherence in the forecasts. Due to the need for transformation to ensure positive forecasts, two data transformations were considered: the logarithm of the number of fire spots plus one and the square root of the number of fire spots plus 0.5. To assess forecast accuracy, the data were split into training data for estimating model parameters and test data for evaluating forecast accuracy. The results show that the ARIMA model with the logarithmic transformation provides overall better forecast accuracy. The BU, MinT(s), and WLS(v) yielded the best results among the reconciliation techniques.

A Bayesian approach to analyzing long-term agricultural experiments

Effective and flexible statistical analyses are key to getting the most out of long-term experiments (LTEs). Here, we aim to introduce Bayesian analysis to the wider LTE community and show how the modelling process differs from traditional statistical analyses. Bayesian methods have become increasingly popular due to more flexibility in model development with better access to statistical software and sampling algorithms. Using Bayes' Theorem, model coefficients are estimated by incorporating any prior knowledge we may have on model terms. Including prior knowledge in this way requires a different estimating procedure for a fitted model. Bayesian model coefficients are usually sampled from thousands of samples from one or more runs of a Markov Chain. We present the use of Bayesian analyses through three examples. Example 1 illustrates a single regression with and without factors using the Broadbalk Long-Term Experiment, showing how the estimated model changes with more uncertainty in our prior knowledge of model coefficients. Example 2 demonstrates the use of multiple regression, predicting grain yield from factor variables and seasonal weather variables. Example 3 shows an estimation of soil carbon changes under crop rotation and fertilization treatments with a hierarchical time series model using a Swedish soil fertility experiment.

A Bayesian Interrupted Time Series framework for evaluating policy change on mental well-being: An application to England’s welfare reform

Factors contributing to social inequalities are associated with negative mental health outcomes and disparities in mental well-being. We propose a Bayesian hierarchical controlled interrupted time series to evaluate the impact of policies on population well-being whilst accounting for spatial and temporal patterns. Using data from the UKs Household Longitudinal Study, we apply this framework to evaluate the impact of the UKs welfare reform implemented in the 2010s on the mental health of the participants, measured using the GHQ-12 index. Our findings indicate that the reform led to a 2.36% (95% CrI: 0.57%–4.37%) increase in the national GHQ-12 index in the exposed group, after adjustment for the control group. Moreover, the geographical areas that experienced the largest increase in the GHQ-12 index are from more disadvantage backgrounds than affluent backgrounds.

Lessons learned: Using a Three-Step Model of Planned Change for nursing curricular revision

BackgroundThe American Association of Colleges of Nursing (AACN, 2021) introduced “The Essentials: Core Competencies for Professional Nursing Education” (Essentials) in 2021. The AACN document necessitated a change in nursing curriculums, both undergraduate and graduate. To meet the revised standards, one college of nursing within a hierarchical organization used a Three-Step Model of Planned Change to guide curricular revisions. This article presents the lessons learned from using the Three-Step Model of Planned Change, which includes barriers, strategies, and a toolkit for implementing planned change. Step One-Desire a ChangeLessons learned include embracing the unifying values of the guiding coalition to understand the motivation(s) and urgency for change. Suggested strategies include creating a cross-sectional organizational team, utilizing collaborative approaches that value members' time, and various communication methods. Step Two-Make the ChangeLessons learned include understanding the larger hierarchical structure's process requirements and time allotment for approval. Suggested strategies include establishing a repository hub for templates and shared documents, implementing various communication channels, and repurposing standing meeting times. Step Three-Live the ChangeAs this process is just beginning, anticipated lessons include an understanding of changes occurring circuitously within and between steps. Considerations include significant and purposeful actions to deliver the new curriculum.

The impact of aragonite saturation variability on shelled pteropods: An attribution study in the California Current System.

Observations from the California Current System (CalCS) indicate that the long-term trend in ocean acidification (OA) and the naturally occurring corrosive conditions for the CaCO3 mineral aragonite (saturation state Ω < 1) have a damaging effect on shelled pteropods, a keystone group of calcifying organisms in the CalCS. Concern is heightened by recent findings suggesting that shell formation and developmental progress are already impacted when Ω falls below 1.5. Here, we quantify the impact of low Ω conditions on pteropods using an individual-based model (IBM) with life-stage-specific mortality, growth, and behavior in a high-resolution regional hindcast simulation of the CalCS between 1984 and 2019. Special attention is paid to attributing this impact to different processes that lead to such low Ω conditions, namely natural variability, long-term trend, and extreme events. We find that much of the observed damage in the CalCS, and specifically >70% of the shell CaCO3 loss, is due to the pteropods' exposure to naturally occurring low Ω conditions as a result of their diel vertical migration (DVM). Over the hindcast period, their exposure to damaging waters (Ω < 1.5) increases from 9% to 49%, doubling their shell CaCO3 loss, and increasing their mortality by ~40%. Most of this increased exposure is due to the shoaling of low Ω waters driven by the long-term trend in OA. Extreme OA events amplify this increase by ~40%. Our approach can quantify the health of pteropod populations under shifting environmental conditions, and attribute changes in fitness or population structure to changes in the stressor landscape across hierarchical time scales.

Discrete forecast reconciliation

This paper presents a formal framework and proposes algorithms to extend forecast reconciliation to discrete-valued data, including low counts. A novel method is introduced based on recasting the optimisation of scoring rules as an assignment problem, which is solved using quadratic programming. The proposed framework produces coherent joint probabilistic forecasts for count hierarchical time series. Two discrete reconciliation algorithms are also proposed and compared against generalisations of the top-down and bottom-up approaches for count data. Two simulation experiments and two empirical examples are conducted to validate that the proposed reconciliation algorithms improve forecast accuracy. The empirical applications are forecasting criminal offences in Washington D.C. and product unit sales in the M5 dataset. Compared to benchmarks, the proposed framework shows superior performance in both simulations and empirical studies.

How to mine the abnormal information of power transformers: An efficient tool for quantifying the fault characteristics via multi-vibration signals

The new power system puts forward higher requirements for the reliability of power equipment. Mining the intrinsic information of equipment operation from massive data is the key challenge to determining fault early warning. The transformer fault diagnosis through vibration signal analysis has gained increasing prominence. However, the vibration signals produced by power transformers exhibit complex nonlinear and multivariate fluctuations due to the interaction of electromagnetic and mechanical factors. Unfortunately, the traditional fault diagnosis models lack the capability to capture extensive global fault information, resulting in inadequate performance in fault identification. This paper proposes the enhanced hierarchical multivariate multiscale fuzzy entropy (EHMvMFE) as an effective method for quantifying defect information in multivariate transformer signals to overcome the challenge. Firstly, the enhanced hierarchical decomposition method and time series coarse-graining theory are introduced into multivariate fuzzy entropy to develop EHMvMFE, which can comprehensively reflect the feature information of multivariate signals from the full range of frequencies. Then, EHMvMFE is utilized to extract the features via multivariate vibration signals of the transformer. Finally, the extreme learning machine is conducted to achieve effective identification of abnormal conditions. The proposed method is applied to two categories of transformer fault cases, and the diagnostic indicators are at least higher than 99.70 % and 91.82 %, which indicates a strong advantage in comparison with other popular models. The approach could be flexibly extended to the fault diagnosis of other power equipment, which is a potentially effective tool for improving the reliability of power systems.

An interpretable multi-scaled agent hierarchy for time series prediction

The traditional time series analysis treats the time series as a dynamic system of sequential entries, leading to complex models and a lack of interpretability. Time series, however, can be understood simply as a composition of correlated information hierarchies in various time scales. Rising from this perspective, here we propose Interpretable multi-time-Scaled Hierarchical Agent-based Time Series Prediction (ISHA-TSP) with linear AutoRegressive (AR) architecture. These time scales, determined based on the instantaneous dominant frequencies of the time series or domain of knowledge, down-sample time series for each agent. Accordingly, a trend prediction signal is offered from a higher time-scale agent to a lower time-scale agent in a hierarchical manner. This hierarchy can also be interpreted reversely, where the lower time-scale agent offers a direction gradient signal to the higher-scale agent to adjust its estimated trend. The optimal learning rate for ISHA-TSP is determined based on a composite Lyapunov function that guarantees convergence. The proposed ISHA-TSP is evaluated with seven datasets in various prediction horizons for accuracy and stop-learning and stop-forecasting steps for robustness. Results show the ISHA-TSP is superior over an equivalent single agent in prediction error. Also, the proposed method adapts against agent failure and data-missing situations. This strategy also leads to simpler models with fewer parameters than a single complex monolithic model. Furthermore, it shows higher interpretability due to its compositional approach.

Considering Nonstationary within Multivariate Time Series with Variational Hierarchical Transformer for Forecasting

The forecasting of Multivariate Time Series (MTS) has long been an important but challenging task. Due to the non-stationary problem across long-distance time steps, previous studies primarily adopt stationarization method to attenuate the non-stationary problem of original series for better predictability. However, existed methods always adopt the stationarized series, which ignore the inherent non-stationarity, and have difficulty in modeling MTS with complex distributions due to the lack of stochasticity. To tackle these problems, we first develop a powerful hierarchical probabilistic generative module to consider the non-stationarity and stochastity characteristics within MTS, and then combine it with transformer for a well-defined variational generative dynamic model named Hierarchical Time series Variational Transformer (HTV-Trans), which recovers the intrinsic non-stationary information into temporal dependencies. Being an powerful probabilistic model, HTV-Trans is utilized to learn expressive representations of MTS and applied to the forecasting tasks. Extensive experiments on diverse datasets show the efficiency of HTV-Trans on MTS forecasting tasks.

Time error accumulation in a hierarchical time and clock distribution network with deterministic optical links

Accurate clock and time distribution is a key requirement for self-triggered streaming data acquisition in the CBM experiment. This distribution is handled by the Timing and Fast Control (TFC) system by clock forwarding and broadcasting the common time over latency-deterministic optical links in a hierarchical FPGA network. The point-to-point optical connections are served by the latency-optimized GBT-FPGA core, which has been developed at CERN. In the presented work, the performance of GBT-FPGA links for time and clock distribution in a scaled TFC system with multiple hops and endpoints has been investigated.

Hierarchical Time Series Forecasting in Emergency Medical Services

Accurate forecasts of ambulance demand are crucial inputs when planning and deploying staff and fleet. Such demand forecasts are required at national, regional, and sub-regional levels and must take account of the nature of incidents and their priorities. These forecasts are often generated independently by different teams within the organization. As a result, forecasts at different levels may be inconsistent, resulting in conflicting decisions and a lack of coherent coordination in the service. To address this issue, we exploit the hierarchical and grouped structure of the demand time series and apply forecast reconciliation methods to generate both point and probabilistic forecasts that are coherent and use all the available data at all levels of disaggregation. The methods are applied to daily incident data from an ambulance service in Great Britain, from October 2015 to July 2019, disaggregated by nature of incident, priority, managing health board, and control area. We use an ensemble of forecasting models and show that the resulting forecasts are better than any individual forecasting model. We validate the forecasting approach using time series cross-validation.

Abstract TP93: A Bayesian Hierarchical Time Series Model to Forecast Patient Recovery Outcomes After an Acute Stroke When Activity Monitor Data is Incomplete

Background: Activity monitor data is a useful tool in clinical trials to monitor patient recovery after stroke. These data offer important information on activity, sedentary and sleep behaviors throughout recovery. However, not all participants wear activity monitors, or their activity data may be incomplete. The purpose of this study was to develop a model-based approach to obtain individual patient-level longitudinal forecast estimates of activity and sleep behaviors for both those with and without complete activity data. Methods: Participants wore an ActivPal (steps/day) and Actigraph (total sleep/day) monitors for 3-7 days at 10-60-90 days post stroke. We developed a Bayesian hierarchical time series model to forecast daily steps and sleep time by participant. We included a logistic growth curve in which we use predictors comprising age, sex, race, marital status, smoking, BMI, cognition, gait speed, depression, self-reported sleep, and patients’ previous time trends to forecast patient specific future time trends during the first 90 days following stroke. Results: Data were collected on a total sample of 114 participants. Out of the 114 participants, 73 participants had recorded sleep data, and 76 participants had step data reported, which are not mutually exclusive groups. Out of 114 total participants, 41 participants did not have any sleep or step data recorded. We obtained patient-specific time trends for both patients with and without monitor data. To assess model predictive performance, we compared predicted estimates to observed data using a validation study and found that on average, there was a difference of 0.52 daily steps (counts). Additionally, on average, there was a difference of 0.46 between observed and estimated daily sleep count (minutes). Discussion: The contribution of our study is a model-based approach to accurately predict patient-specific longitudinal step and sleep behaviors based on predictor variables and previous time trends for patients in the subacute stroke recovery phase. Our approach may be extended to other applications using activity monitor data. A limitation of this study is the increased uncertainty surrounding forecast estimates for periods/days without data, which will be addressed in future work.