Rule-Based Forecasting: Development and Validation of an Expert Systems Approach to Combining Time Series Extrapolations

One of the most important challenges when analyzing and forecasting the time series is the stability of the series and determining components of the time series such as trend and seasonal. Exponential Smoothing methods can be thought of as peers and alternatives to Box-Jenkins ARIMA class of time series forecasting methods, but the most important aspect of the exponential smoothing approach is that the time series does not have to be stable. The study introduces reviewing and comparing a variety of Exponential Smoothing models; Simple Exponential Smoothing (SES), Holt’s Linear Exponential Smoothing or Double Exponential Smoothing (DES) and Holt Winters Algorithm or Triple Exponential Smoothing (TES). Additionally; creation temporal patterns to forecast the monthly stock returns of the Saudi Stock Index by using a variety of Exponential Smoothing models. The results of the study concluded that the Holt Winters Algorithm or triple exponential smoothing model is the best model since it produces the lowest Mean Absolute Percentage error (MAPE), Mean Absolute Deviation (MAD), and Mean Squared Deviation (MSD) values which are 4,380, 244783 compared to 4, 385, 246837 for SES, and 5, 410, 270734 for DES, and thus can be used to predict the monthly stock returns of the Saudi Stock Index.

Introduction:Asthma exacerbations are frequent causes of pediatric hospital admissions. We sought to develop a time series algorithm to forecast next-day daily asthma hospitalizations.Methods:Daily hospitalizations for asthma were collected at Cincinnati Children’s from January 1, 2016, to December 31, 2023. We evaluated Autoregressive Integrated Moving Average (ARIMA), Exponential Smoothing (ETS), Prophet, and Ensemble models to forecast next-day asthma hospitalizations validated on 2023 data, considering varying historical training data lengths. Forecasts were calibrated to identify days exceeding a 5% high-risk threshold of historical totals and considered multiple validation years and years before and during the COVID-19 pandemic.Results:A total of 5,593 hospital admissions were recorded for asthma. Over 2,922 days, 166 days met the 5% high-risk threshold equating to 6 or more admissions. The Ensemble (Median Absolute Percentage Error (MAPE): 46.7%; Positive Predictive Value (PPV): 0.278; Negative Predictive Value (NPV): 0.942; Area Under the ROC Curve (AUC): 0.740; Sensitivity: 0.800; Specificity: 0.656) model achieved higher accuracy of high-risk days than ARIMA (MAPE: 46.5%; PPV: 0.278; NPV: 0.942; AUC: 0.709; Sensitivity: 0.760; Specificity: 0.571), ETS (MAPE: 47.2%; PPV: 0.222; NPV: 0.939; AUC: 0.711; Sensitivity: 0.800; Specificity: 0.668), and Prophet (MAPE: 48.9%; PPV: 0.444; NPV: 0.951; AUC: 0.732; Sensitivity: 0.680; Specificity: 0.741) models.Conclusions:Our Ensemble model of mean predictions from ARIMA, ETS, and Prophet models was the most accurate in forecasting future asthma hospitalizations. Integrating forecasting techniques with clinical operations could enable proactive prevention through enhanced population care management.

Error measures for generalizing about forecasting methods: Empirical comparisons

Pressure gradient (PG) in liquid-liquid flow is one of the key components to design an energy-efficient transportation system for wellbores. This study aims to develop five robust machine learning (ML) algorithms and their fusions for a wide range of flow patterns (FP) regimes. The MLs include Support Vector Machine (SVM), Gaussian Process (GP), Random Forest (RF), Artificial Neural Network (ANN), k-Nearest Neighbor (kNN), and fusions of these five MLs. A total of eleven hundred experimental data points for nine FPs (two stratified and seven dispersed patterns) in horizontal wellbores are used to develop the MLs. The MLs' performance is evaluated using the metrics including mean absolute percentage error (MAPE), median absolute percentage error (MdAPE), coefficient of variation of root mean squared error (CV-RMSE), and adjusted coefficient of determination. The evaluation metrics are cross-validated using a repeated train-test split strategy. Seven important predictor variables are identified using a supervised feature selection approach: oil and water velocities, FP, input diameter, oil and water density, and oil viscosity. The results show that the high PG prediction accuracy can be achieved using GP compared to other MLs except for the ML-fusions (p < 0.05). A Friedman's test and Wilcoxon Sign-Rank post hoc analysis with Bonferroni correction show that PG prediction errors using GP are significantly lower than using the ANN model (p < 0.05). The values are 18.44 % and 23.9 % for CV-RMSE, 11.6 % and 10.06 % for MAPE, and 7.5 % and 6.75 % for MdAPE, using ANN and GP, respectively. While the previous studies mostly used ANN to demonstrate the capability of MLs to predict PG over the mechanistic or correlation-based models, the present research has shown that GP is even better than ANN using a wide range of FPs and a large data set. • Machine-learning algorithms are developed to predict the pressure gradient. • The Gaussian Process model produces significantly lower prediction error. • The median absolute percentage error using Gaussian Process is 6.75 %. • More than 95 % variation of pressure gradient can be explained using seven variables.

In this study, we explore and compare various time series models to forecast OPEC oil prices, aiming to identify the most accurate model for predicting future trends. The methodology involves the application of multiple time series forecasting models, including Random Walk, Linear Trend, Quadratic Trend, Exponential Trend, S-Curve Trend, Simple Moving Average, Simple Exponential Smoothing, Brown's Linear Exponential Smoothing, Holt's Linear Exponential Smoothing, Brown's Quadratic Exponential Smoothing, and ARIMA. Each model is evaluated based on performance metrics such as Root Mean Squared Error (RMSE), Mean Absolute Error (MAE), Mean Absolute Percentage Error (MAPE), Mean Error (ME), Mean Percentage Error (MPE), Akaike Information Criterion (AIC), Hannan-Quinn Criterion (HQC), and Bayesian Information Criterion (BIC) to determine its accuracy and reliability. Among the models tested, the ARIMA(1,1,0) model emerged as the best-performing model, providing the most accurate predictions. Using this model, we forecast OPEC oil prices for a 12-month period from July 2024 to May 2025. Our findings include detailed forecasts for each month within this period, offering valuable insights for policymakers and market participants. These results highlight the importance of selecting an appropriate time series model to improve forecasting accuracy and inform decision-making processes in the energy sector.

This study examines whether the improvement in analyst forecast accuracy around mandatory IFRS adoption is associated with the improvement in the accuracy of financial statement-based forecasts. We find significant out-of-sample improvement in financial statement-based forecast accuracy around mandatory IFRS adoption and significant improvement in analyst forecast accuracy only in countries that made concurrent improvements to financial reporting enforcement. We show that the improvement in analyst forecast accuracy is associated with the improvement in financial statement-based forecast accuracy around IFRS adoption. We also show that analyst forecasts, particularly for firms whose analysts forecast under favorable conditions (i.e., analysts who are less busy with more experience and resources), have a greater association with financial statement-based forecasts, after mandatory IFRS adoption in countries with concurrent changes in enforcement.

Forecasting of economic indicators with time series using one or another method or another but the only method leads to the situation that all the information contained in other forecasting methods is usually discarded. The information that is ignored may contain information that allows other features of the economic process to be assessed. Combining forecasts makes possible to take into account almost all the information contained in particular forecasts. In the article, we present the analysis of the application of the method of regression analysis, in particular, ridge regression for finding the weighting coefficients of the particular forecasts in the combined forecast. We compared the accuracy of prediction based on the ridge regression with other methods of combining predictions. The purpose of our research work was an analysis of the most common methods of combining forecasts — various modifications of Granger-Ramanathan methods and comparison with a new approach of combining forecasts based on the ridge regression for its use in practice. We used statistical methods of time series forecasting (the method of harmonic weights, adaptive exponential smoothing using a tracking signal, the method of simple exponential smoothing and the Box-Jenkins model), the method of constructing combined forecasts, as well as methods of regression analysis. As a result, we built the combined forecasts based on annual data for the period from 1950 to 2015 on the production in Russia of some products: steel, metallurgical coke, pulp, plywood, cement. We used the methods of Granger-Ramanathan (without restrictions and with restrictions on the sum of coefficients in partial predictions) and also the ∆-coefficients obtained by the ridge regression method. The forecasts constructed using the Granger-Ramanathan methods give the highest accuracy of the combined forecast. The method based on the ridge regression is less accurate, but better than the separate predictions. At the same time, the proposed method of calculating the weight coefficients on the basis of the ridge regression has a well- developed scheme of calculation and eliminates the negative weight coefficients in the combined forecast.

Calibration and Validation of the Youth Activity Profile: The FLASHE Study.

Predicting housing prices in China based on modified Holt's exponential smoothing incorporating whale optimization algorithm

Power system state estimation is one of the most important functions of power system control centers. In recent years, the complexity of power system state estimation has significantly increased due to the growing number of distributed, including renewable energy sources, electric vehicles, the demand response technologies, and the increased risk of cyber-attacks. Under these conditions, state estimation methods, which consider information about the time-correlation of the power system states have a great potential. The correlation is described by a transition model. The well-known state estimation methods usually use one single model. However, in case of stochastic behavior of the load and generation, it is impossible to assert the adequacy of the chosen model over the entire observation interval. Therefore, the paper proposes a multi-model forecasting power system state estimation method, which has lower errors in comparison with a single-model assessment at the moments of the lowest accuracy of the latter. Multi-model parameter estimation is used based on three procedures of the single-model Kalman filtering estimation and various transition models based on autoregressive and vector autoregressive analyzes, as well as Holt's exponential smoothing. Uniting the single-model estimation has been carried out according to the criterion of the minimum of variance of the resulting estimate. An algorithm of multi-model power system state estimation has been developed. Its version has been analyzed using a three-model forecasting-aided estimation using linear transition models. The state of the IEEE 30-bus test power system has been assessed by the means of simulation modeling. The maximum accuracy increase of the multi-model estimation in comparison with the single model is set up. 26,1 % is for autoregressive analysis; 16,9 % is for vector regression analysis and 37,7 % is for Holt’s exponential smoothing. The proposed method of multi-model state estimation has higher robustness and accuracy at the moments of the lowest accuracy of single-model estimation. It is advisable to use the method to solve control tasks of power systems with rapidly changing dynamic modes.

Hepatitis B (HB) is a major global mortality. Accurately predicting the trend of the disease can provide an appropriate view to make health policy disease prevention. This paper aimed to apply three different to predict monthly incidence rates of HB. This historical cohort study was conducted on the HB incidence data of Hamadan Province, the west of Iran, from 2004 to 2012. Weighted Markov Chain (WMC) method based on Markov chain theory and two time series models including Holt Exponential Smoothing (HES) and SARIMA were applied on the data. The results of different applied methods were compared to correct percentages of predicted incidence rates. The monthly incidence rates were clustered into two clusters as state of Markov chain. The correct predicted percentage of the first and second clusters for WMC, HES and SARIMA methods was (100, 0), (84, 67) and (79, 47) respectively. The overall incidence rate of HBV is estimated to decrease over time. The comparison of results of the three models indicated that in respect to existing seasonality trend and non-stationarity, the HES had the most accurate prediction of the incidence rates.

Fuzzy time series (FTS) is a method of making educated guesses by using fuzzy intervals, which correspond to time series clusters. It is also useful for data noise reduction and is based on rule-based forecasting. The aim of this article is to develop a vector autoregressive fuzzy integrated logical forecasting (VAR-FILF) model for time charter rates of Panamax and Handymax bulk carriers. Results are tested by using Chen's FTS method (cFTS), bivariate cFTS (Bi-cFTS) method and conventional time series methods, and the accuracy of the VAR-FILF method is found to be higher than these methods. In addition, the length of intervals affects the forecasting result and the accuracy of forecasting. Therefore, this study proposes the fuzzy C-means clustering method for the structuring of the fuzzy length of intervals of the FTS forecasting process.

This study addresses the crucial need for accurate forecasting of Foreign Direct Investment (FDIT) trends in Nigeria. FDIT plays a pivotal role in the country's economic growth and development efforts, driving industrialization, infrastructure enhancement, and job creation. However, predicting FDIT accurately is essential for policymakers, investors, and researchers to formulate effective strategies and decisions. This study conducts a comparative analysis of four FDIT forecasting models: Simple Exponential Smoothing (SES), Holt Exponential Smoothing (HES), ARIMA, and NNAR in Nigeria, utilizing R version 4.3.2 and forecast and nnetar packages for implementation. The FDIT dataset is partitioned into 80:20 training-test samples, with models applied to each subset for performance evaluation. Leveraging historical FDIT data, the study evaluates the predictive performance of each model over a specified period, employing error measures such as RMSE, MAE, MASE and MAPE to assess accuracy and reliability. Additionally, residual normality tests and visual inspections validate model assumptions. Results indicate varying levels of accuracy and predictive capability among the models, with HES and NNAR models displaying superior performance compared to SES and ARIMA, evidenced by measure error rates. Residual normality tests affirm the suitability of the models for FDIT forecasting. The study contributes empirical evidence to the existing literature, providing valuable insights into forecasting techniques for FDIT in Nigeria. These insights can guide policymakers, investors, and researchers in selecting appropriate models for forecasting FDIT trends and making informed decisions. Future research avenues could explore advanced modelling techniques and additional variables to further enhance the accuracy and reliability of FDIT forecasts within the Nigerian context.

Objective: Consensus continuous glucose monitoring (CGM) guidance includes a recommendation that a minimum of 14 days of CGM data are used to report times in ranges. The previously employed approaches to determine the optimal duration for CGM data have limitations. In this study, we present a robust approach to define the minimum duration of CGM data to report times in ranges, as well as other glycemic metrics. Methods: The approach is based on the median absolute percentage error and employs a sliding time window to reduce the impact of inter-time interval variability, hence allowing smaller data sets to be used. A 10% and 5% threshold were employed to assess the optimal duration of CGM data for a set of commonly employed metrics to assess quality of glycemic control and glycemic variability. To evaluate the impact of the data set size and type of intervention, data from two randomized controlled trials involving participants with type 1 diabetes were used (n = 236 and n = 25). Results: Results suggest that mean glucose reaches the 5% threshold for mean absolute percentage error within 2 weeks, whereas percentage time in target 70-180 mg/dL, mean absolute glucose, standard deviation, and coefficient of variation reach the same threshold within 4 weeks in both data sets, suggesting that these metrics can be robustly assessed from CGM data for a 4-week period, whereas some other metrics require much longer window lengths, especially those evaluating hypoglycemia. Conclusions: Our data suggest that there is no optimal duration for CGM data to robustly assess all outcomes and that the duration required for a robust outcome depends on the population being studied, the sampling frequency, and the primary outcomes selected.

Performance prediction is an active area of research due to its applicability in the advancements of hardware-software co-development. Several empirical machine-learning models, such as linear models, non-linear models, probabilistic models, tree-based models and, neural networks, are used for performance prediction. Furthermore, the prediction model's accuracy may vary depending on performance data gathered for different software types (compute-bound, memory-bound) and different hardware (simulation-based or physical systems). We have examined fourteen machine-learning models on simulation-based hardware and physical systems by executing several benchmark programs with different computation and data access patterns. Our results show that the tree-based machine-learning models outperform all other models with median absolute percentage error (MedAPE) of less than 5% followed by bagging and boosting models that help to improve weak learners. We have also observed that prediction accuracy is higher on simulation-based hardware due to its deterministic nature as compared to physical systems. Moreover, in physical systems, the prediction accuracy of memory-bound algorithms is higher as compared to compute-bound algorithms due to manufacturer variability in processors.