Holt-Winters Exponential Smoothing Research Articles

On Integrating Time-Series Modeling with Long Short-Term Memory and Bayesian Optimization: A Comparative Analysis for Photovoltaic Power Forecasting

The means of energy generation are rapidly progressing as production shifts from a centralized model to a fully decentralized one that relies on renewable energy sources. Energy generation is intermittent and difficult to control owing to the high variability in the weather parameters. Consequently, accurate forecasting has gained increased significance in ensuring a balance between energy supply and demand with maximum efficiency and sustainability. Despite numerous studies on this issue, large sample datasets and measurements of meteorological variables at plant sites are generally required to obtain a higher prediction accuracy. In practical applications, we often encounter the problem of insufficient sample data, which makes it challenging to accurately forecast energy production with limited data. The Holt–Winters exponential smoothing method is a statistical tool that is frequently employed to forecast periodic series, owing to its low demand for training data and high forecasting accuracy. However, this model has limitations, particularly when handling time-series analysis for long-horizon predictions. To overcome this shortcoming, this study proposes an integrated approach that combines the Holt–Winters exponential smoothing method with long short-term memory and Bayesian optimization to handle long-range dependencies. For illustrative purposes, this new method is applied to forecast rooftop photovoltaic production in a real-world case study, where it is assumed that measurements of meteorological variables (such as solar irradiance and temperature) at the plant site are not available. Through our analysis, we found that by utilizing these methods in combination, we can develop more accurate and reliable forecasting models that can inform decision-making and resource management in this field.

COVID-19 Case Growth Prediction Using a Hybrid Fuzzy Time Series Forecasting Model and a Machine Learning Approach

The COVID-19 pandemic has evolved into a global health crisis, with Indonesia particularly affected due to its high death rates compared to the rest of Asia. A significant number of unacknowledged, undocumented, or unaddressed cases further exacerbate the situation in Indonesia. Challenges arise from the growing patient population and a scarcity of resources, medical experts, and facilities. This study analyzes the daily development of COVID-19 cases in Indonesia, aiming to estimate the number of confirmed cases, recoveries, and fatalities. Introducing a novel hybrid forecasting model, we utilize the Holt-Winter triple exponential smoothing statistical method and the fuzzy time series rate of change algorithm. We apply the Triple Exponential Smoothing Holt Winter statistical model to predict future periods to the fuzzy time series. Based on the testing results, our proposed hybrid forecasting model demonstrates a very high level of predictive capacity. The acquired data are highly accurate, with a 0.15 percent confirmation rate, 0.15 percent recovery rate, and a 0.20 percent mortality rate, along with an average absolute error of less than 10% for each COVID-19 case. The findings indicate that early awareness by the COVID-19 Task Force of the status of cases is highly advantageous. This awareness can aid in formulating appropriate policies for future planning, organization, and accelerated treatment of COVID-19 in Indonesia. Consequently, successful efforts can be made to slow the emergence and spread of COVID-19 in the country.

Msf, a forecasting library to predict short-term electricity demand based on multiple seasonal time series

Transmission system operators have a growing need for more accurate forecasting of electricity demand. Current electricity systems largely require demand forecasting so that the electricity market establishes electricity prices as well as the programming of production units. The companies that are part of the electrical system use exclusive software to obtain predictions, based on the use of time series and prediction tools, whether statistical or artificial intelligence. However, the most common form of prediction is based on hybrid models that use both technologies. In any case, it is software with a complicated structure, with a large number of associated variables and that requires a high computational load to make predictions. On many occasions, the resources to reach these predictions are not available to researchers. In this paper we present a MATLAB® toolbox created to predict electrical demand. The toolbox implements multiple seasonal time series forecasting methods such as new generalized multiple seasonal Holt–Winters exponential smoothing models and neural network models, among others. The models presented include novel discrete interval mobile seasonalities (DIMS) to improve forecasting on special days. The paper also describes the computational analysis conducted to apply the toolbox in various electrical systems in Europe, where the results obtained can be seen. The use of this library opens a new way of research for the use of models with discrete and complex seasonalities in other fields of application.

Analysis and Forecasting of Consumer Price Index (CPI) in Kenya and South Africa using Holt Winter Model

In this paper, Holt-Winters exponential smoothing approach is applied to model and forecast monthly CPI in Kenya and South Africa. Monthly data from January 2000 to December 2023 was obtained from Central Bank of Kenya and South Africa department of statistics. Time series decomposition showed that the trend component is the most dominant component in both countries. Kenya Holt-Winters estimated model has parameters 0.6756, 0.0077 and 1 for level smoothing, trend smoothing and seasonal smoothing respectively. On the other hand, South Africa estimated model has parameters 0.8917, 0.1057 and 1 for level smoothing, trend smoothing and seasonal smoothing respectively. The estimated models are efficient and effective as on average the fitted values are less than one percent off the observed values. The initial values for level smoothing, trend smoothing and seasonal smoothing are approximately equal in both countries. The estimated models are then used to predict CPI next twelve months. Over the forecast period, South Africa will experience a lower index as compared to Kenya. In both countries, it’s expected that monthly CPI will rise.

FORECASTING THE NUMBER OF AIRPLANE PASSENGERS USING HOLT WINTER'S EXPONENTIAL SMOOTHING METHOD AND EXTREME LEARNING MACHINE METHOD

Airplanes provide comfort and speed for their users, especially for those who have limited time. The number of passengers has continued to increase in the last few months at Ahmad Yani International Airport, so a forecast is needed in making decisions to predict the number of passengers in order to maximize existing performance. The data used is secondary data on the number of airplane passengers at Ahmad Yani International Airport from 2012 to 2022 obtained from PT Angkasa Pura 1 (Persero). The Holt Winters Exponential Smoothing method is used because it aligns with the data pattern that includes trends and seasonality in the research, and it has a low level of accuracy. In this study also used the Extreme Learning Machine (ELM) method, apart from being a relatively new method, it has a fast learning speed and has low accuracy. This study aims to predict the number of airplane passengers at Ahmad Yani International Airport in Semarang using the Holt Winters Exponential Smoothing and ELM methods. The results of the analysis show that the MAPE value in the Holt Winters Exponential Smoothing method is 8,18% and in the ELM method using 12 input neurons and 43 neurons in the hidden layer, a MAPE of 6,04% is obtained. so that the ELM method is the right method for predicting the number of airplane passengers at Ahmad Yani International Airport in Semarang.

Forecasting Rice Prices with Holt-Winter Exponential Smoothing Model

Rice, as a staple food, plays a crucial role in global food security. Accurate forecasting of rice prices is essential for policymakers, farmers, and consumers alike. This article explores the application of the Holt-Winter exponential smoothing model to predict rice prices. Holt-Winter method is chosen for its ability to capture both trend and seasonality in time series data, which are prominent features in agricultural commodity prices such as rice. The study analyzes historical price data, identifies trends, seasonality, and incorporates smoothing parameters in additive and multiplicative methods. Results indicate that additive method of Holt-Winter exponential smoothing provides a better performance. This research contributes valuable insights to the field of agricultural economics and informs strategies for managing food supply chains and market stability.

Impact of COVID-19 pandemic in the Brazilian maternal mortality ratio: A comparative analysis of Neural Networks Autoregression, Holt-Winters exponential smoothing, and Autoregressive Integrated Moving Average models.

The acute respiratory infection caused by severe acute respiratory syndrome coronavirus disease (COVID-19) has resulted in increased mortality among pregnant, puerperal, and neonates. Brazil has the highest number of maternal deaths and a distressing fatality rate of 7.2%, more than double the country's current mortality rate of 2.8%. This study investigates the impact of the COVID-19 pandemic on the Brazilian Maternal Mortality Ratio (BMMR) and forecasts the BMMR up to 2025. To assess the impact of the COVID-19 pandemic on the BMMR, we employed Holt-Winters, Autoregressive Integrated Moving Average (ARIMA), and Neural Networks Autoregression (NNA). We utilized a retrospective time series spanning twenty-five years (1996-2021) to forecast the BMMR under both a COVID-19 pandemic scenario and a controlled COVID-19 scenario. Brazil consistently exhibited high maternal mortality values (mean BMMR [1996-2019] = 57.99 ±6.34/100,000 live births) according to World Health Organization criteria. The country experienced its highest mortality peak in the historical BMMR series in the second quarter of 2021 (197.75/100,000 live births), representing a more than 200% increase compared to the previous period. Holt-Winter and ARIMA models demonstrated better agreement with prediction results beyond the sample data, although NNA provided a better fit to previous data. Our study revealed an increase in BMMR and its temporal correlation with COVID-19 incidence. Additionally, it showed that Holt-Winter and ARIMA models can be employed for BMMR forecasting with lower errors. This information can assist governments and public health agencies in making timely and informed decisions.

Deep learning-based air pollution analysis on carbon monoxide in Taiwan

Global air pollution poses a threat to humanity. Specifically, CO directly affects cardiovascular and other organ tissues and leads to numerous chronic diseases and major public health problems. The effective implementation of a deep learning model for predicting variations in CO levels would enable the early formulation of policies for controlling air pollution. In this study, a seasonal gated recurrent unit (SGRU) model, which is a deep learning time-series prediction model, was developed to predict the levels of CO in Taiwan. Atmospheric CO measurements from 2005 to 2021 were collected from the Environmental Protection Administration of Taiwan and preprocessed using the Kalman filter to achieve accurate forecasting. The performance of the proposed SGRU model was compared with that of the autoregressive integrated moving average (ARIMA), seasonal ARIMA, exponential smoothing (ETS), Holt–Winters ETS, support vector regression, and seasonal long short-term memory models in terms of mean absolute percentage error (MAPE) and root mean square error. The SGRU model achieved the lowest MAPE value of 0.94, which demonstrated its superior performance. The construction of an accurate air pollution prediction model can assist government entities in formulating health and social care strategies and in planning future air pollution control measures.

Application of Holt-Winter Exponential Smoothing Method to Design a Drug Inventory Prediction Application in Private Health Units

This research aims to see how to design a drug supply prediction application using the Holt-Winter Exponential Smoothing method. The collection methods used in the research are as follows: observation, interviews. The prototyping system development method includes several important stages in designing research applications. The first stage is communication. After that, the Quick Plan stage. Construction of prototype stages. The final stage, deployment delivery and feedback, is the phase of system use by users. In addition, the team also conducts regular system maintenance to ensure optimal performance. These stages together form an iterative process for developing research applications using the prototyping method. Based on the research results, it was found that the test results for the drugs amoxicillin, cefixime, paracetamol, and CTM showed that the MAPE value was less than 10% for these four drugs, which means that the predictive value has quite high accuracy. So it can be concluded that the Holt Winter Exponential Smoothing algorithm can be well implemented to predict drug supplies.

Forecasting COVID-19 Daily Infected Cases in Sri Lanka by Holt-Winters Exponential Smoothing Method

The novel coronavirus disease (COVID-19) has spread from China since December 2019 and spread worldwide including Sri Lanka. The aim of this study was to forecast the daily infected cases of COVID-19 in Sri Lanka which in turn help administrators for effective management of the pandemic. The method used in this study was Holt-Winters three parameter with additive or multiplicative models. The daily infected cases in Sri Lanka during the period of 22nd January 2020 to 22nd December 2021 were obtained from the publicly available databases of Epidemiology Unit of Sri Lanka and World Health Organization. The pattern recognition of the daily infected cases was examined by time series plot and Auto Correlation Function (ACF). The model validation was performed by the Anderson Darling test which confirmed the normality of residuals (p > 0.05) and ACF that confirmed the independence of residuals of the model. The forecasting ability of the model was assessed by the three measurements of errors; Mean Absolute Percentage Error (MAPE), Mean Absolute Deviation (MAD) and Mean Square Error (MSE). Holt-Winters additive and multiplicative model with α (level) 0.61, β (trend) 0.4 and γ (seasonal) 0.3 at a length of repeating behaviour of 3 days, had the least relative and absolute measurement of errors during the model fitting and verification. İn the multiplicative model, MAPE, MAD and MSE were 0.2847, 0.0187 and 0.0005 respectively. Similarly in the additive model, corresponding values of MAPE, MAD and MSE were 0.0207, 0.0187 and 0.0005. The fits and the forecast of these models followed a similar pattern of the actual daily infected cases concluding that the Holt-Winters model can be used to forecast the COVID-19 outbreak in Sri Lanka.

İnşaat Maliyet Endeksi Tahmininde Holt-Winters Üstel Düzeltme Parametrelerinin PSO ve İleri Walk-Forward Cross-Validation ile Optimizasyonu

This research aims to enhance the accuracy of Construction Cost Index (CCI) forecasting using Holt-Winters exponential smoothing (ES) by optimizing its parameters, focusing on minimizing the Mean Absolute Percentage Error (MAPE) for precise CCI forecasts. To reach this aim, The Holt-Winters model parameters are optimized through Particle Swarm Optimization (PSO) and Walk-Forward Cross-Validation (WFCV). PSO, a metaheuristic optimization algorithm, is being applied to search for optimal values of the smoothing parameters (alpha, beta, and gamma) that determine the weightage of past observations, trends, and seasonality, respectively. WFCV is assessed the model's performance and ensures robustness. Reduced MAPEs of 22 for CCI forecasts and 2 for training data are the findings of the optimized Holt-Winters model. The obtained alpha, beta, and gamma values are 0.99, 0.77, and 0, respectively, highlighting the importance of while neglecting seasonality. Convergence graphs demonstrate the superiority of the optimization approach over conventional parameter values or random selections. By employing PSO and WFCV, the study efficiently fine-tunes the Holt-Winters model for precise CCI forecasting. Optimized parameter values enable data driven decision-making in construction project cost estimation and budget management. This research contributes a reliable and robust optimization methodology for CCI forecasting, supporting advancements in the field.

Multidimensional analysis of losses in the number of passengers transported by air in Poland and Germany caused by the COVID-19 pandemic in terms of the maintenance of economic security

In the study, the authors conducted a multidimensional data analysis on the decrease in the number of passengers transported by air in Poland and Germany caused by the COVID-19 pandemic between 2020-2022. Forecasts of the number of passengers transported by air in Poland and Germany obtained after applying the Holt-Winters exponential smoothing method from January 2020 to December 2022 were compared with actual data. The research showed that in the case of Germany, in 2020 there was a decrease of 174 628 873 people, and in 2022, it was 90 620 354 people. In Poland, the decrease in 2020 amounted to 40 257 520 people; in 2022, it was already 21 083 066 passengers.

Analysis and Forecasting of Solar Power Generation using Machine Learning

Current photovoltaic systems are equipped with a monitoring system. The data is recorded with a predefined time base. The operator has a large amount of data. This article is a contribution to the analysis and understanding of this data. It proposes to estimate Generation from this data using machine learning. The study was conducted at the 1Mw generation site in Miroslava, Iasi, Romania. The visualization and interpretation of the generation data is presented in this article. Then, prediction techniques are presented to obtain an estimate of the plant’s generation. These techniques are: Simple Exponential Smoothing (SES), Autoregression (AR), Seasonal Auto-Regressive Integrated Moving Average with eXogenous factors (SARIMA), Holt Winter’s Exponential Smoothing (HWES), Long Short Term Memory neural (LSTM) and Convolutional Neural Network (CNN).

Analysis of road accident mortality based on time of occurrence for Kerala, India

Background: Road traffic accidents (RTA) pose a significant socio-economic burden and global public health concern. Monitoring road safety initiatives' efficacy necessitates analysing RTA incidence. This study examines time zone-specific RTA mortality in Kerala state, India, from 2016 to 2021. Methods: Utilizing compiled secondary-level time series data, the study encompasses total RTA fatalities in Kerala from 2016 to 2021. Data includes fatalities per year in nine consecutive three-hour time periods. Exploratory data analysis, time series regression, and exponential smoothing were employed for analysis. Results: Data reveals fluctuating trends in road accident (RA) fatalities, peaking in 2018 with a notable decrease in 2020. 18:00 to 21:00 recorded the highest and lowest fatalities, total 901 deaths. Disproportionate RA fatalities occurred from 06:00 to 09:00 (527 deaths) and 15:00 to 18:00 (697.5 deaths). The study employs Holt-Winters exponential smoothing for short-term forecasting, with a mean absolute scaled error (MASE) less than 1 signifying accurate predictions. Conclusions: The analysis highlights temporal patterns, emphasizing 18:00 to 21:00 as critical. Holt-Winters exponential smoothing proves vital for accurate short-term forecasting, with MASE reflecting precision. Urgency is stressed in adopting targeted measures for time-specific road accidents. Government intervention is pivotal, advocating for improved infrastructure, enhanced driver education, efficient vehicle management, and sustained traffic enforcement. Tailoring traffic laws to time zones, coupled with forecasting techniques, aligns with the overarching goal of enhancing road safety and reducing RA mortality rates.

Modelling Risk for Commodities in Brazil: An Application for Live Cattle Spot and Futures Prices

This study analyses a series of live cattle spot and futures prices from the Boi Gordo Index (BGI) in Brazil. The objective is to develop a model that best portrays this commodity’s behaviour to estimate futures prices more accurately. The database created contains 2010 daily entries in which trade in futures contracts occurs, as well as BGI spot sales in the market, from 1 December 2006 to 30 April 2015. One of the most important reasons why this type of risk needs to be measured is to set loss limits. To identify patterns in price behaviour in order to improve future transaction results, investors must analyse fluctuations in asset values for longer periods. Bibliographic research reveals that no other study has conducted a comprehensive analysis of this commodity using this approach. Cattle ranching is big business in Brazil given that in 2021, this sector moved BRL 913.14 billion (USD 169.29 billion). In that year, agribusiness contributed 26.6% of Brazil’s total gross domestic product. Using the proposed risk modelling technique, economic agents can make the best decision about which options within these investors’ reach produce more effective risk management. The methodology is based on Holt–Winters exponential smoothing algorithm, autoregressive integrated moving-average (ARIMA), ARIMA with exogenous inputs, generalised autoregressive conditionally heteroskedastic and generalised autoregressive moving-average (GARMA) models. More specifically, five different methods are applied that allow a comparison of 12 different models as ways to portray and predict the BGI commodity behaviours. The results show that GARMA with order c(2,1) and without intercept is the best model. Investors equipped with such precise modelling insights stand at an advantageous position in the market, promoting informed investment decisions and optimising returns.

Leveraging Classical Statistical Methods for Sustainable Maintenance in Automotive Assembly Equipment

Predictive maintenance management plays a crucial role in ensuring the reliable operation of equipment in industry. While continuous monitoring technology is available today, equipment without sensors limits continuous equipment state data recording. Predictive maintenance has been effectively carried out using artificial intelligence algorithms for datasets with sufficient data. However, replicating these results with limited data is challenging. This work proposes the use of time series models to implement predictive maintenance in the equipment of an automotive assembly company with few records available. For this purpose, three models are explored—Holt–Winters Exponential Smoothing (HWES), Autoregressive Integrated Moving Average (ARIMA), and Seasonal Autoregressive Integrated Moving Average (SARIMA)—to determine the most accurate forecasting of future equipment downtime and advocate the use of SAP PM for effective maintenance process management. The data were obtained from five equipment families from January 2020 to December 2022, representing 36 registers for each piece of equipment. After data fitting and forecasting, the results indicate that the SARIMA model best fits seasonal characteristics, and the forecasting offers valuable information to help in decision-making to avoid equipment downtime, despite having the highest error. The results were less favorable when handling datasets with random components, requiring model recalibration for short-term forecasting.

Trend of the Tuberculous Pleurisy Notification Rate in Eastern China During 2017-2021: Spatiotemporal Analysis.

Tuberculous pleurisy (TP) presents a serious allergic reaction in the pleura caused by Mycobacterium tuberculosis; however, few studies have described its spatial epidemiological characteristics in eastern China. This study aimed to determine the epidemiological distribution of TP and predict its further development in Zhejiang Province. Data on all notified cases of TP in Zhejiang Province, China, from 2017 to 2021 were collected from the existing tuberculosis information management system. Analyses, including spatial autocorrelation and spatial-temporal scan analysis, were performed to identify hot spots and clusters, respectively. The prediction of TP prevalence was performed using the seasonal autoregressive integrated moving average (SARIMA), Holt-Winters exponential smoothing, and Prophet models using R (The R Foundation) and Python (Python Software Foundation). The average notification rate of TP in Zhejiang Province was 7.06 cases per 100,000 population, peaking in the summer. The male-to-female ratio was 2.18:1. In terms of geographical distribution, clusters of cases were observed in the western part of Zhejiang Province, including parts of Hangzhou, Quzhou, Jinhua, Lishui, Wenzhou, and Taizhou city. Spatial-temporal analysis identified 1 most likely cluster and 4 secondary clusters. The Holt-Winters model outperformed the SARIMA and Prophet models in predicting the trend in TP prevalence. The western region of Zhejiang Province had the highest risk of TP. Comprehensive interventions, such as chest x-ray screening and symptom screening, should be reinforced to improve early identification. Additionally, a more systematic assessment of the prevalence trend of TP should include more predictors.

Analisis Model Manajemen Permintaan SCM dan Peramalan Penjualan Busana Menggunakan Metode Holt-Winter Exponential Smoothing

Sales forecasting is a highly crucial strategy in the business world, as it significantly contributes to enhancing a company's profits. In this context, sales transaction forecasting plays a vital role in assisting business decision-makers in planning effective sales strategies. The utilization of the Holt-Winters Exponential Smoothing method in sales forecasting demonstrates an effective approach. In this study, this method was applied to retail sales data of Muslim clothing from 2021 to 2023. By setting the parameters ? = 0.9, ? = 0.1, and ? = 0.1, the forecasting results indicate a high level of accuracy with low values for Mean Squared Error (MSE), Root Mean Squared Error (RMSE), and Mean Absolute Percentage Error (MAPE), amounting to 29.93, 295.93, and 0.62%, respectively. Consequently, the forecast reveals that the inventory of clothing for periods 13 to 16 is 83, 228, 129, and 115, respectively

Implementation of Holt-Winter Exponential Smoothing Method to Forecast The Spread of Covid-19

This research examines the Holt winters exponential smoothing method to solve forecasting problems using case studies of the spread of Covid-19. The data source uses the transmission of Covid-19 in Indonesia. MAPE is used to measure errors in data forecasting. The results are structured to serve as a recommendation for other researchers in choosing a method for predicting the spread of the disease. Based on the results, forecasting with the Holt-Winters model in positive cases produces a MAPE value of 9.21% using the Multiplicative model and the best parameter values of alpha, beta and gamma (0.4, 0.05, 0.25). Whereas in the case of human recovery, the MAPE value was 11.86% using the Multiplicative model and the best values for the parameters alpha, beta and gamma (0.4, 0.03, 0.1). And in the case of death it produces a MAPE of 17.97% using the Multiplicative model and the parameter values alpha, beta and gamma (0.4, 0.01, 0.1). So, it can be concluded that the Holt-Winters method on human positive case data shows a good outcome performance while recovered and deceased cases produce a well-being analysis performance.

STORAGE SERVER DATABASE UTILIZATION FORECASTING USING HOLT-WINTERS AND ARIMA METHODS IN E-GOVERNMENT SYSTEM. STUDY AT KEMENKEU RI

Storage is a storage medium which is an important part of the system infrastructure. Storage utilization is one of the variables in determining the needs and performance of a system. If the storage is lacking or depleted it will cause the system to be hampered and the possibility of interference occurring. There were eight complaints or reports of system disturbances recorded in the Ministry of Finance's ticketing service desk application caused by anomalies in storage or disk capacity. Things like this can be anticipated if we know the storage capacity requirements for the future. In compiling ICT capacity analysis at Pusintek there has been no use of past data to plan future storage requirements. The use of data mining algorithms can be used to obtain forecast values from storage utilization. The use of the ARIMA model and Holt-Winters Exponential Smoothing as a method used to predict inventory is considered to be a fairly accurate model. Both algorithms are used to compare which accuracy is better in predicting storage requirements by measuring RMSE. Research data was obtained from monthly utilization reports from January 2021 to December 2022. From the evaluation results it can be concluded that forecasting storage server database utilization using the Holt-Winters method is better than the ARIMA method with the RMSE results for the Holt-Winters method being 14332.661717740748 and the RMSE method ARIMA is 20498.977982137938. The results of this forecasting can be utilized in planning database server storage needs.