Holt Model Research Articles

Machine Learning Algorithms Based on Time Series Pre-Clustering for Nocturnal Glucose Prediction in People with Type 1 Diabetes.

Background: Machine learning offers new options for glucose prediction and real-time glucose management. The aim of this study was to develop a machine learning-based algorithm that takes into account glucose dynamics patterns for predicting nocturnal glucose in individuals with type 1 diabetes. Methods: To identify glucose patterns, we applied a hierarchical clustering algorithm to real-time continuous glucose monitoring data obtained from 570 adult patients. Machine learning algorithms with or without pre-clustering were used for modeling. Results: Eight clusters without nocturnal hypoglycemia and six clusters with at least one low-glucose episode were identified by the cluster analysis. When forecasting time series without hypoglycemia with a prediction horizon (PH) of 15 or 30 min, gradient boosting trees (GBTs) with pre-clustering and random forest (RF) with pre-clustering outperformed algorithms based on medoids of time series clusters, the Holt model, and GBTs without pre-clustering. When forecasting time series with low-glucose episodes, a model based on the pre-clustering and GBTs provided the highest predictive accuracy at PH = 15 min, and a model based on RF with pre-clustering was the best at PH = 30 min. Conclusions: The results indicate that the clustering of glucose dynamics can enhance the efficacy of machine learning algorithms used for glucose prediction.

Local population dynamics of gray wolves Canis lupus and Eurasian lynx Lynx lynx exhibit consistency with intraspecific contest competition models

AbstractIn Europe, the gray wolf and Eurasian lynx populations are recovering after various levels of persecution. The two species differ in their social structure and spatial patterns of aggregation. Using model selection, we investigated the consistency of the available time series data on local wolf and lynx sub‐populations with a number of single‐species population growth models that pertain to two types of intraspecific competition, namely, scramble (SC) and contest competition (CC), and reflect random (R) or aggregated (A) distribution of individuals. The applied models of population growth—the Ricker (SCR), Skellam (CCR), Hassell (SCA), and Beverton–Holt (CCA) models—were all parameterized in terms of intrinsic growth rate and carrying capacity with unified definitions. The projected carrying capacity was allowed to show a temporal trend, which was justified by an observed increase in prey abundance in recent decades. For both species, the models pertaining to contest competition outperformed the scramble competition models, and the Beverton–Holt model had the greatest weight. However, for the lynx, the difference of performance between the scramble and contest competition models was considerably smaller than that for the wolves. In most of the models, when it was meaningful, an optional time lag operator was added to account for a delay in individual maturity and reproduction. However, the models with a time lag had a worse fit than the models without it. This study promotes the application of population models that reflect intraspecific competition for modeling population dynamics in a single‐ or multi‐species framework.

Development and Comparison of InSAR-Based Land Subsidence Prediction Models

Land subsidence caused by human engineering activities is a serious problem worldwide. We selected Qian’an County as the study area to explore the evolution of land subsidence and predict its deformation trend. This study utilized synthetic aperture radar interferometry (InSAR) technology to process 64 Sentinel-1 data covering the area, and high-precision and high-resolution surface deformation data from January 2017 to December 2021 were obtained to analyze the deformation characteristics and evolution of land subsidence. Then, land subsidence was predicted using the intelligence neural network theory, machine learning methods, time-series prediction models, dynamic data processing techniques, and engineering geology of ground subsidence. This study developed three time-series prediction models: a support vector regression (SVR), a Holt Exponential Smoothing (Holt) model, and multi-layer perceptron (MLP) models. A time-series prediction analysis was conducted using the surface deformation data of the subsidence funnel area of Zhouzi Village, Qian’an County. In addition, the advantages and disadvantages of the three models were compared and analyzed. The results show that the three developed time-series data prediction models can effectively capture the time-series-related characteristics of surface deformation in the study area. The SVR and Holt models are suitable for analyzing fewer external interference factors and shorter periods, while the MLP model has high accuracy and universality, making it suitable for predicting both short-term and long-term surface deformation. Ultimately, our results are valuable for further research on land subsidence prediction.

Derivation and dynamics of discrete population models with distributed delay in reproduction

We introduce a class of discrete single species models with distributed delay in the reproductive process and a cohort dependent survival function that accounts for survival pressure during that delay period. These delay recurrences track the mature population for species in which individuals reach maturity after at least τ and at most τ+τM breeding cycles. Under realistic model assumptions, we prove the existence of a critical delay threshold, τ˜c. For given delay kernel length τM, if each individual takes at least τ˜c time units to reach maturity, then the population is predicted to go extinct. We show that the positive equilibrium is decreasing in both τ and τM. In the case of a constant reproductive rate, we provide an equation to determine τ˜c for fixed τM, and similarly, provide a lower bound on the kernel length, τ˜M for fixed τ such that the population goes extinct if τM≥τ˜M. We compare these critical thresholds for different maturation distributions and show that if all else is the same, to avoid extinction it is best if all individuals in the population have the shortest delay possible. We apply the model derivation to a Beverton–Holt model and discuss its global dynamics. For this model with kernels that share the same mean delay, we show that populations with the largest variance in the time required to reach maturity have higher population levels and lower chances of extinction.

Forecasting Inflation Rates in Zambia: Time Series Analysis with the Holt Model

Forecasting Inflation Rates in Zambia: Time Series Analysis with the Holt Model

Generalized periodicity and applications to logistic growth

Classically, a continuous function f:R→R is periodic if there exists an ω>0 such that f(t+ω)=f(t) for all t∈R. The extension of this precise definition to functions f:Z→R is straightforward. However, in the so-called quantum case, where f:qN0→R (q>1), or more general isolated time scales, a different definition of periodicity is needed. A recently introduced definition of periodicity for such general isolated time scales, including the quantum calculus, not only addressed this gap but also inspired this work. We now return to the continuous case and present the concept of ν-periodicity that connects these different formulations of periodicity for general discrete time domains with the continuous domain. Our definition of ν-periodicity preserves crucial translation invariant properties of integrals over ν-periodic functions and, for ν(t)=t+ω, ν-periodicity is equivalent to the classical periodicity condition with period ω. We use the classification of ν-periodic functions to discuss the existence and uniqueness of ν-periodic solutions to linear homogeneous and nonhomogeneous differential equations. If ν(t)=t+ω, our results coincide with the results known for periodic differential equations. By using our concept of ν-periodicity, we gain new insights into the classes of solutions to linear nonautonomous differential equations. We also investigate the existence, uniqueness, and global stability of ν-periodic solutions to the nonlinear logistic model and apply it to generalize the Cushing–Henson conjectures, originally formulated for the discrete Beverton–Holt model.

Growth parameters and stock assessment of Carangoides bajad Forsskal, 1775 (Carangiformes: Carangidae) in Jeddah fisheries

ABSTRACT The stock status of Carangoides bajad in Jeddah fisheries was assessed by estimating the growth parameters, mortality rates and size at first capture (Lc), then applying the results to estimate the yield and biomass per recruit. The length-weight relationship could be described by the power equation: W = 0.011 L3.019 (R2 = 0.99) for combined sexes. Von Bertalanffy Growth Parameters L∞, K and t0 were estimated to be 71.53 cm, 0.224 year −1, and −0.52 year, respectively. The total, natural, fishing mortality coefficients and exploitation were calculated to be 0.72 year −1, 0.337 year −1, 0.383 year −1, and 0.53 year −1, respectively. Beverton and Holt (1957) model was used to estimate the yield and biomass per recruit at Fcur and Lc and found to be Y/R = 291 g and B/R = 759 g. Compared with the two biological reference points Fmax = 0.56 year −1 and F0.1 = 0.346 year −1, the Fcur value was very close to the F0.1 value required to get the optimum Y/R. We recommend avoiding any increase in Fcur, and increasing Lc to be 38 centimetres to increase the B/R from 759 g to 793 g, which would increase the probability of sustaining sufficient recruitment to the fishery of C. bajad in Jeddah fisheries.

Analysis of Periodic and Seasonal Characteristics in Time Series: Taking the Dow Jones Industrial Average as an Example

The objective of this research is to conduct a comprehensive analysis of the Dow Jones Industrial Average (DJIA) with a focus on identifying cyclical and seasonal patterns observed in long-term time series data. In order to accurately predict future market trends, this research employs a combination of fundamental and advanced forecasting techniques, including mean, naive, snaive, drift, Holt, Holt-Winters, and ARIMA models. Furthermore, the research explores the impact of return ratios on market investment opportunities. Customized portfolio optimization strategies are developed based on the risk profiles of different investors, along with quantitative trading strategies that effectively manage market risks using the Capital Asset Pricing Model (CAPM). The research shows that the price of Dow Jones Industrial Index has a gradual upward trend, and its return rate has a certain periodicity and seasonality. The aim of this research is to provide valuable insights into the fundamental framework of the American stock market, enabling economists, investors, and policymakers to make informed decisions.

The HWAM-EMD-GRU Forecasting Model for Short-Term Passenger Flow in an Airport Light Rail Transit Line

Accurate forecasting of airport light rail transit line (ALRTL) outbound passenger flow is critical to the optimal operations of both light rail and airport systems. Considering the nonlinearity, non-stationarity, uncertainty, and periodicity of outbound passenger flow in the ALRTL, we propose a combined forecasting model that integrates the Holt and Winters additive model (HWAM), empirical mode decomposition (EMD) and gated recurrent unit (GRU). Firstly, the edge effect of EMD will greatly affect the performance of the forecasting model. To overcome this, we extend the passenger flow by HWAM. After that, the decomposition method, EMD, can be applied to passenger flow, and several intrinsic mode function (IMF) components can be extracted. After extracting all the IMFs, the remaining part is referred to as the residual (Res) component. Then, a correlation test is performed on all the components, followed by their aggregation. Finally, the GRU is used to predict each of the aggregated components, and the prediction of aggregated components requires reconstruction. To verify the performance of the HWAM-EMD-GRU, we conducted a comparative study on the hourly passenger flow data for Beijing Daxing International Airport Express and set the autoregressive integrated moving average model, HWAM, Prophet, and GRU as the baseline. Predictions of the HWAM-EMD-GRU combined model demonstrated higher accuracy than baseline models, with a root mean square error of 83.52 (Prophet is 110.21) and mean absolute percentage error of 8.32% (Prophet is 12.48 %). The experimental result shows that the HWAM-EMD-GRU forecasting model offers more accurate predictions.

Utilization Trends of Phosphodiesterase Type-5 Inhibitors for Erectile Dysfunction Between 2019 and 2023 in Tanzania.

Introduction Erectile dysfunction (ED) profoundly affects millions of people globally, including interfering with mental health and quality of life. Phosphodiesterase type-5 inhibitors (PDE5Is) such as sildenafil are pivotal in ED treatment. This study aimed to examine the utilization patterns ofPDE5Is in Tanzania. Materials and methods In this retrospective longitudinal study, data on sildenafil and other similar PDE5Is imported between 2019 and 2023 were sourced from the Tanzania Medicines and Medical Devices Authority (TMDA). Pre-processing and visualization were performed using Microsoft Power BI Desktop, and further analysis was performed using IBM SPSS Statistics for Windows, Version 26 (Released 2019; IBM Corp., Armonk, New York, United States). Utilization trends were ascertained through curve fitting, Holt's linear trend model, and autoregressive integrated moving average (ARIMA) models. The defined daily doses (DDDS) per 1000 inhabitants (DID) were calculated using the World Health Organization (WHO) Anatomical Therapeutic Chemical (ATC) Classification System and the DDD methodology endorsed by the WHO Collaborating Centre for Drug Statistics Methodology. Results Between 2019 and 2023, there was a pronounced increase in the importation of approximately 587 consignments of PDE5Is. Employing the Holt model (R-square = 0.843), a substantial increase from 0.220910 DID in 2019 to 0.534272 DID by 2025 was observed and anticipated. The period witnessed sildenafil dominating 75.5% of the total use, with Erecto being the most consumed brand (37.6% of totalDID). Notably, 2022 had the highest surge (27.2% of the total), albeit a slight decline was observed in 2023 (20.5%). This trend was supported by a linear regression model (R-square = 0.889). Conclusion We found increasing annual trends of PDE5Is of utilization. This requires critical oversight and effective policies to ensure appropriate use and risk minimization.

Optimizing Inventory Management of MFD Studio To Reduce The High Lost Sales

This research delves into optimizing inventory management at MFD Studio by implementing demand forecasting to mitigate lost sales. Notably, the company has encountered a significant loss of sales, approximately 31.26% of the revenue generated by their flagship product, Outer, which has consistently held the position of the best-seller from 2021 to 2023, contributing approximately 60% to MFD Studio's overall product line during this period. The research aims to enhance inventory management efficiency by employing demand forecasting techniques. The methodology includes a thorough literature review, analysis of root causes, and conceptual framework development. The findings underscore the substantial impact of demand forecasting on inventory management, leading to a noteworthy reduction in lost sales. The study advocates for adopting a quantitative approach to demand forecasting, explicitly endorsing the ARIMA, Holt, and Winter models. Notably, the ARIMA model stands out with the lowest error, boasting a 0.0059 RMSE value, 0.0025 MAE value, and 0.0363 MAPE value. The forecast generated by the ARIMA model is anticipated to diminish the likelihood of future lost sales to 5.5%, representing a substantial decrease from the initial 31.26%. In conclusion, this research underscores the pivotal role of demand forecasting as a crucial tool for businesses, particularly in similar industries, to enhance inventory management and curtail lost sales. The practical recommendations contribute significantly to inventory management, offering actionable insights for businesses seeking to optimize their inventory processes.

Modeling and Forecasting of Coconut Area, Production, and Productivity Using a Time Series Model

The study aimed to compare ARIMA and Holt's models for predicting coconut metrics in Kerala. The coconut data series was collected from the period 1957 to 2019. Of this, 80% of the data (from 1957 to 2007) is treated as training data, and the rest (20% from 2008 to 2019) is treated as testing data. Ideal models were selected based on lower AIC and BIC values. Their accuracy was evaluated through error estimation on testing data, revealing Holt's exponential, linear, and ARIMA (0,1,0) models as the bestfit choices for predicting coconut area, production, and productivity respectively. After using the testing data, we tried for the forecasting for 2020-2024 using these models, and the DM test confirmed their significant forecasting accuracy. This comprehensive analysis provides valuable insights into effective prediction models for coconut-related metrics, offering a foundation for informed decision-making and future projections.

On a Coupled Time-Varying Beverton–Holt Model with Two Habitats Subject to Harvesting, Repopulation, and Mixed Migratory Flows of Populations

Two time-varying Beverton–Holt models are investigated in which the population of the same species evolves jointly in two coupled habitats which can be subject to population exchanges. Both habitats can have different parameterizations concerning their intrinsic growth rates and their environment carrying capacities due to different environmental conditions. Mutual fluxes of populations in-between both habitats are possible together with harvesting actions. In one of the models harvesting acts on juvenile individuals. In the other proposed model, harvesting takes place on the adult populations after the reproduction cycle they have performed has ended. The second investigated model, contrarily to the first one, relies on an “a posteriori” harvesting action to the reproductive stage which is able to modify the stocks of population. The considered harvesting can also be negative to describe repopulation actions. The equilibrium points in steady-state and their stability properties as well as the extinction conditions and the boundedness, oscillation issues, and positivity of the solutions are also investigated.

A Darwinian Beverton–Holt model with immigration effect

In this study, we investigate the dynamics of a discrete-time evolutionary Beverton–Holt model under the immigration effect. The model tracks the dynamics of the population, coupled with that of the population mean trait. By using the center manifold theorem and bifurcation theory, we establish that the system undergoes Neimark–Sacker and period-doubling bifurcations when the immigration effect passes some critical values. Bifurcation diagrams, maximum Lyapunov exponents, and time series are examples of numerical simulations that not only illustrate our theoretical analysis but also show the complicated dynamical behaviors of this model. Furthermore, we applied the hybrid control method and the exponential method to achieve the asymptotic stability of an unstable equilibrium.

Application of Multivariate Modelling to Global Warming Projections

Global warming is a natural phenomenon in which the accumulation of energy in the Earth's atmospheric system leads to an increase in temperature. To build the model, we collected multiple datasets from the 20th century: average annual global temperatures, average monthly temperatures at different latitudes, global losses from various natural disasters, global emissions of various chemicals, and population. We then pre-processed and visualized the data. In our quantitative analysis, we found that the increase in global temperature in March 2022 did not exceed the increase in the past 10 years. We then developed three models to describe past and project future global temperature levels: the GM(1,1) model, the ARIMA(0,1,1) model, and the Holt model. By primarily comparing the fit of the three models, we concluded that the Holt model has the highest prediction accuracy. We found that the relationship between time and global temperature.

The Efficiency of Solid Waste Logistics Management: A Prominent Case Study of Banped Subdistrict, Municipality Mueang Khon Kaen District, Khon Kaen Province

Solid waste is a significant issue worldwide, and it is concerned by many countries worldwide. Local government has a substantial role in managing solid waste. Solid waste is increasing yearly because of several causes, such as the rapidly rising population and the massive city's expansion into suburban areas. The Municipal takes responsibility to collect and dispose of the solid waste in their responsible area. This article aims to forecast solid waste in the future using four methods: static methods, exponential smoothing, Holt's model, and Winter's model. Then, compare all methods to find the optimal ones with the most accurate forecasting. By determining the criteria, the forecast error measures are the absolute deviation (MAD) and the mean of the absolute percentage error (MAPE), which have a minimum error. One of the other purposes is to develop an optimization route that provides the possibility of decreasing distances and reducing transportation expenses. Typically, the most common methods are the Traveling Salesman Problem (TSP) and Vehicle Routing Problem (VRP) to solve the problems. This article will use two algorithms for two steps. The first step is to set the routes with the nearest neighbor heuristic (NN) to generate the routes MSW from point to point until all are reached and return to the origin point. In the second step, improve the routes by using the 2-Opt heuristic. The results found that the 2-Opt can decrease transportation distances, which is optimal and saves costs. In addition to that, it can make process management more effective. Keywords: Forecasting, Nearest Neighbour Heuristic, 2-Opt Heuristic, Travelling Salesman Problem

Forecasting the renewable energy consumption of Australia by a novel grey model with conformable fractional opposite-direction accumulation.

The accurate prediction of renewable energy consumption (REC) is of great significance to ensure energy security, reduce dependence on fossil energy, and promote sustainable economic and social development. In this paper, a novel grey model with conformable fractional opposite-direction accumulation (CFOA), abbreviated as the CFOGM (1,1) model, is proposed to forecast REC in Australia. The new model is discussed in detail with a new CFOA operation and the GM (1,1) model and can take full advantage of the information carried by the original data. The CFOGM (1,1) model has lower modeling error and better fitting and forecasting accuracy than other grey, Holt, and ARM models and can better capture the change trend of REC and achieve accurate prediction. The forecasting results present that the REC in Australia is 497-581 petajoules in 2021, 596-728 petajoules in 2022, and 715-912 petajoules in 2023, indicating that the REC in Australia is still accelerating.

A combined model of Hawkes-ICEEMDAN-Catboost-Holt for interval-valued carbon price forecasting

Accurate carbon price forecasting is crucial for efficiently operating both carbon trading and financial markets. This study proposes a Hawkes-ICEEMDAN-Catboost-Holt combined interval forecasting model to improve the accuracy of carbon price forecasts. First, the t-SNE-LLE second-order dimensionality reduction was performed on the collected search index data to quantify the attention of netizens. Subsequently, the attention series was converted into an interval series using the Hawkes exponential decay model, and further decomposed into radius and center series. In addition, the radius and center series were decomposed using ICEEMDAN and then reconstructed. Finally, the carbon price interval combined forecast was based on the Catboost–Holt model. The proposed model exhibits high accuracy and strong stability in comparison to other forecast models. The Hawkes exponential decay of netizens’ attention is creatively included in the influence mechanism of carbon price fluctuations, effectively improving forecast accuracy. The interval decomposition and reconstruction methods provide an innovative development path for interval forecasting research. The residual and trend series obtained from interval reconstruction can be forecasted using Catboost and Holt, respectively, thus significantly improving the accuracy and stability of interval forecasts and enhancing the decision-making process for carbon trading and financial markets.

Application of Adaptive and Multiplicative Models for Analysis and Forecasting of Time Series

The paper considers two forms of models: seasonal and non-seasonal analogues of oscillations. Additive models belong to the first form, which reflects a relatively constant seasonal wave, as well as a wave that dynamically changes depending on the trend. The second ones are multiplicative models. The paper analyzes the basic adaptive models: Brown, Holt and autoregression models. The parameters of adaptation and layout are considered by the method of numerical estimation of parameters. The mechanism of reflection of oscillatory (seasonal or cyclic) development of the studied process through reproduction of the scheme of moving average and the scheme of autoregression is analyzed. The paper determines the optimal value of the smoothing coefficient through adaptive polynomial models of the first and second order. Prediction using the Winters model (exponential smoothing with multiplicative seasonality and linear growth) is proposed. The application of the Winters model allows us to determine the calculated values and forecast using the model of exponential smoothing with multiplicative seasonality and linear growth. The results are calculated according to the model of exponential smoothing and with the multiplicative seasonality of Winters. The best model is determined, which allows improving the forecast results through the correct selection of the optimal value of α. The paper also forecasts the production volume according to the Tayle-Vage model, i.e., the analysis of exponential smoothing with additive seasonality and linear growth is given to determine the calculated values α. The paper proves that the additive model makes it possible to build a model with multiplicative seasonality and exponential tendency. The paper proves statements that allow one to choose the right method for better modeling and forecasting of data.

Reliability Evaluation of Radial Distribution Feeder Considering Two Load Modelling of Forecasted Electric Vehicle Load

The use of an electric vehicle (EV) in place of an internal combustion engine reduces pollution and produces zero emissions. EVs need considerable electrical energy from the grid, and therefore it is necessary to evaluate the performance of the radial distribution system, including the Electrical Vehicle Charging Station (EVCS) load. The future EVCS load is forecasted using Holt's model, and then it is applied uniformly to the distribution system. This increases the magnitudes of currents, which are calculated using the backward and forward sweep method of load flow analysis. The increased magnitude of current moderates the operating temperature of the components and results in an increase in the average failure rate of feeder line sections. The percentage change in the average failure rate is assumed to be directly proportional to the percentage change in current, which in turn affects reliability indices such as SAIDI and ENS. The reliability analysis needs proper modelling of loads on the system and is taken as light and heavy load, considered this as two load model. The existing load without EVs of the distribution system is taken as a light load and the future load including the EV load during the charging period (5hrs) on the distribution system is taken as a heavy load. In this paper, the reliability indices of a radial distribution feeder are calculated for different cases like without EV load, with EV load and for different percentages of faults during EV load duration and the results are compared. This work is validated on IEEE33 standard distribution system.