Time series air quality forecasting with R Language and R Studio

Stock market volatility is important for investment, option pricing and financial market regulation. In recent years, stock market analysis and prediction have the greatest significance for many professionals in the fields of finance and stock exchange. There are many methods available in the literature to solve the problem of future prediction. The present study provides a detailed comparison of Single Exponential Smoothing (SES) model and Autoregressive Integrated Moving Average (ARIMA) model. Future values are forecasting using SES and ARIMA model. Forecasted values for different iś values are calculated from SES method and ARIMA (0, 2, 3). Also, Mean Square Error (MSE), Mean Absolute Deviation (MAD), Root Mean Square (RMSE) and Mean Absolute Percentage Error (MAPE) are calculated individually for both methods.

A single prediction method has its own advantages and disadvantages in different aspects. In order to improve the accuracy of water level prediction, a water level prediction method combining The Autoregressive Integrated Moving Average (ARIMA) Model, Exponential Smoothing (ES) model and Long Short-term Memory (LSTM) model through nonlinear programming genetic algorithm is proposed in this paper. By combining the advantages of local search of nonlinear programming and global search of genetic algorithm, this method uses nonlinear programming genetic algorithm to allocate the weights of ARIMA model, ES model and LSTM model, and obtains the final water level prediction result by weighting. The empirical results show that this method not only has higher prediction accuracy than single model, but also has higher prediction accuracy than using nonlinear programming or genetic algorithm to allocate weight.

Household saving rate is an indispensable reference for people to grasp household economic behavior and analyze macroeconomic trends, and has a significant impact on capital accumulation, consumption and policy design. Taking UK household saving rate as the research object, this study compares the forecasting ability of Autoregressive Integrated Moving Average (ARIMA) model and Exponential Smoothing (ETS) model systematically based on the quarterly data from 2007Q1 to 2025Q1. Due to the economic fluctuations shown in UK from 2007Q1 to 2025Q1, it is particularly valuable to identify a robust model to forecast it. The empirical results show that the ETS (M, N, M) model is more robust than ARIMA (1,0,0) model in terms of root mean square error (RMSE), mean absolute error (MAE) and mean absolute percentage error (MAPE) in out-of-sample forecasting. The in-sample fit of ARIMA model is better, but it may be over-fitted. This study can provide a reliable basis for the model selection of forecasting UK household saving rate, and the methodological approach and research conclusions of this study are also available for other similar countries.

This study aims to (i) develop predictive models using statistical and fuzzy approaches, and (ii) evaluate their forecasting performance. The data were obtained from www.investing.com for the period 1961 to 2017 and focus on five ASEAN countries: Indonesia, Malaysia, the Philippines, Singapore, and Thailand. The statistical models used are Autoregressive Integrated Moving Average (ARIMA) and Exponential Smoothing, while the fuzzy approaches include Chen and Singh fuzzy time series models. The dataset was divided into training and test sets in a 75%-25% proportion. ARIMA models capture trends and autocorrelations in time series data, while Exponential Smoothing uses exponentially weighted averages. Fuzzy models are designed to handle uncertainty and linguistic patterns in data. The results show that Singh’s fuzzy model yields the lowest error for Indonesia, while exponential smoothing and Chen fuzzy time series model demonstrate the same lowest error for Malaysia. For the Philippines, exponential smoothing is most accurate, whereas ARIMA and Singh fuzzy time series achieve the smallest error for Singapore. For Thailand, exponential smoothing and ARIMA perform equally well. However, the robustness of the forecasting model cannot be determined from either statistical or fuzzy methods, highlighting the challenge in determining the most robust model for inflation in the ASEAN region. The 75%-25% data split may also limit the generalizability of the findings. This study contributes a rare cross-country comparison of statistical and fuzzy forecasting methods in the ASEAN context. It highlights the importance of model selection based on country-specific inflation behavior and provides insights for improving forecasting strategies in macroeconomic applications.

In this study, four conventional and a newly proposed method of wavelet-exponential smoothing (WES) - with two presented scenarios (WES1 and WES2) – are employed to estimate daily and monthly suspended sediment load (SSL) in two rivers (Lighvanchai river in Iran and Upper Rio Grande in the USA), which have different hydro-geomorphological characteristics of the related watersheds. In the proposed WES method, first, wavelet transform (WT) is applied to the original observed time series to decompose them into approximation and detailed subseries to separate different components of time series. For the first scenario (WES1), only two time series, i.e., an approximation and a detail time series are utilized as inputs of model, whereas for the second scenario (WES2), all subseries are separately fed into different exponential smoothing (ES) models. The results revealed that for both rivers, the proposed WES2 and wavelet based artificial neural network (WANN) models could lead to superior performance in comparison to the autoregressive integrated moving average (ARIMA), seasonal ARIMA (SARIMA), ES ad-hoc and artificial neural network (ANN). The WES2 method could enhance the overall performance of SSL forecasting both in daily and monthly modeling of the case studies regarding Nash-Sutcliffe (E) efficiency criteria, respectively up to 13%, 42% and 87%, 116% in daily and monthly scales for SSL modeling of the Lighvanchai and Upper Rio Grande Rivers. As a result, combining WT with ES method and ANN led to more accurate modeling.

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.

This paper proposes the Exponential Smoothing Model, Frequency Probability Model, and Logistic Regression Model, focusing on the prediction methods of multiple models in scenarios with varying data characteristics. First, for scenarios with large datasets or stable trends, the Exponential Smoothing Model is introduced. It captures trend changes through weighted averages of historical data (with higher weights assigned to more recent data) and, through cross-validation, determines the parameters to predict future total and categorized quantities of the target object while analyzing their changing trends. Next, for scenarios with smaller datasets or larger fluctuations, the Frequency Probability Model is used, estimating future probabilities based on the frequency of historical events. By comparing data at different stages of typical cases, the model quantifies the impact of specific factors on increasing the probability of an event occurring. Finally, for zero-sample scenarios, the Logistic Regression Model is constructed, incorporating variables such as participant scale and historical participation frequency. Adaptive optimization algorithms are used to solve the parameters and predict the probability of first-time events, identifying high-potential objects and fields, and providing recommendations for resource allocation. The Exponential Smoothing Model is effective for predicting stable data, the Frequency Probability Model quantifies the probability characteristics of repeatable events, and the Logistic Regression Model provides a multi-factor probability prediction framework for zero-sample scenarios. Together, the three models offer diverse predictive approaches for different data characteristic scenarios.

BackgroundRed blood cells (RBCs) infusion is very important for the treatment of hematology patients, but how to maintain a balanced state between the supply and demand of RBCs is still a major challenge.ObjectiveThis study aimed to explore the feasibility of seasonal autoregressive integrated moving average (SARIMA) model and exponential smoothing (ES) model in predicting the clinical demand of RBCs for hematology patients each month.MethodsOur study collected the monthly RBCs usage data of hematology patients from January 2014 to December 2023 to establish the SARIMA model and ES model, respectively. Then, the optimal model was used to forecast the monthly usage of RBCs from January to June 2024, and we subsequently compared the data with actual values to evaluate the prediction effect of the model.ResultsThe best fitting SARIMA model was SARIMA (2,1,0)(1,1,1)12, whose R2 = 0.603, MAE = 37.092, MAPE = 13.693, BIC = 7.896. The best fitting ES model was Winters addition model, whose R2 = 0.702, MAE = 32.617, MAPE = 12.138, BIC = 7.485. The mean relative errors of two models were 0.085 and 0.159, respectively. The SARIMA (2,1,0)(1,1,1)12 model performed better in prediction.ConclusionCompared with the ES model, the SARIMA model has a smaller mean relative error in predicting RBCs usage in hematology patients. DM test also verify this result. But in the future, more similar research data are needed to make research more convincing.

Oil prices have an impact on the global economy. Demand shocks, such as those caused by the recent COVID-19 epidemic, or supply shocks caused by production reductions by major global producers, result in sudden price changes. Oil industry has been collecting price data since the late 19th century. A time series of this magnitude allows for consistent analysis of price behavior forecasts following demand or supply shocks. Financial time series are sensitive to exogenous shocks. From this perspective, this work presents a comparative analysis of predictive crude oil prices scenarios, obtained from a historical series of average annual prices. Two approaches were used: first, a combination of classic strategies based on exponential smoothing, and ARIMA models. Second, an autoregressive neural network model. Both approaches are complementary when used for long-term forecasting of oil prices and show good response to volatile data. Therefore, we are able to present an alternative data analysis, in a field where there is a great amount of relevant historical series, using probabilistic and non-linear models in order to observe predictions and make more effective decisions.

An experimental comparison of exponential and adaptive smoothing forecasting models using actual operating data

Indonesia targets Aceh to be one of the paddy production centers and be able to carry out self-sufficient production in paddy and become a national granary. However, in reality, Aceh's paddy production in its province is not consistent from year to year. This province has not been able to meet the food needs of paddy independently, so that it supplies paddy from other regions due to the difficulty of detecting the presence of a surplus of paddy. The purpose of this research is to estimate the results of paddy production in Aceh for the future. The mathematical model that can be used is a time series model namely Autoregressive Integrated Moving Average (ARIMA) and Exponential Smoothing. The results of the estimation of paddy production in the next 5 years using the ARIMA (1,1,3) model are 2000616; 2017549; 1903585; 1944499; and 1929810. While the estimation results using the Winter Exponential Smoothing model are 1625925; 1645196; 1687667; 1605530; and 1555213. ARIMA model (1,1,3) produces an MSE/MAD value of , while the Winter Exponential Smoothing model produces an MSE/MAD value of . Therefore, it can be concluded that the Winter Exponential Smoothing model.

The inflation rate, particularly in South Sulawesi Province from year to year, is found to be very unstable, so that an effort to overcome the instability of the inflation rate is highly needed. One of the efforts that can be used is to carry out a process of forecasting the inflation rate, so that the government can predict the inflation rate properly in order to realize the sustainable economic growth. The aim of this study was to forecast Inflation Cases in South Sulawesi Province. The forecasting carried out in this study used the Exponential Smoothing method. Exponential Smoothing is a method that will take into account average (smoothing) the data of the past exponentially by repeating calculations continuously using the latest data. In this study, 2 Exponential Smoothing methods were compared, namely: Single Exponential Smoothing (SES) and Double Exponential Smoothing (DES) which were used to obtain prediction results and evaluate the results of predictions using the Mean Square Error (MSE) and Mean Absolute Percentage Error (MAPE) methods. The smallest MAPE value was obtained when using the Single Exponential Smoothing (SES) method when the value ɑ = 0.1 with the MSE value of 0.5567 and MAPE value of 265.7126 and the Double Exponential Smoothing (DES) method when the value ɑ = 0.3 and with the MSE value of 4,256 and MAPE value of 574,519. Thus, the Single Exponential Smoothing (SES) method was regarded as the best method in predicting the inflation rate in South Sulawesi Province.

The increasing demand for elephant healthcare in Thailand underscores the need for efficient resource management in veterinary hospitals. Treating sick elephants requires substantial medical inputs, and without accurate workload forecasting, hospitals risk shortages in staff, equipment, and medications, potentially compromising care quality. This study evaluated six time-series forecasting models— Autoregressive Integrated Moving Average and its seasonal model (ARIMA/SARIMA), Exponential Smoothing (ETS), Trigonometric, Box-Cox ARMA Trend Seasonality (TBATS), Neural Network Time Series Regression (NNTR), Prophet, and Extreme Gradient Boosting (XGBoost)—to predict monthly workloads at two major elephant hospitals: the National Elephant Institute (NEI) hospital in northern Thailand and the Department of Livestock Development (DLD) hospital in the northeast. Historical admission data spanning five years (NEI) and nine years (DLD) were analyzed. The ETS model achieved the highest accuracy at NEI, outperforming all other models by effectively capturing its stable and seasonal caseload patterns. In contrast, the NNTR model performed best at DLD, where it accommodated irregular fluctuations likely driven by external factors. Forecasts for 2025 suggested a consistent caseload at NEI (28–31 cases/month) and a declining trend at DLD, with the lowest projection in September. Although patient volume was low, each case demanded disproportionately high resources, justifying the need for anticipatory planning. This study provides the first demonstration that multi-model time-series forecasting can generate actionable insights using sparse, real-world data from wildlife hospitals. By embedding predictive analytics into routine operations, it offers a novel, scalable framework to support data-driven decision-making in endangered species care.

The Auto Regressive Integrated Moving Average (ARIMA) model seems not to easily capture the nonlinear patterns exhibited by the 2019 novel coronavirus (COVID-19) in terms of daily confirmed cases. As a result, Artificial Neural Network (ANN) and Error, Trend, and Seasonality (ETS) modeling have been successfully applied to resolve problems with nonlinear estimation. Our research suggests that it would be ideal to use a single model of ETS or ARIMA for COVID-19 time series forecasting rather than a complicated Hybrid model that combines several models. We compare the forecasting performance of these models using real, worldwide, daily COVID-19 data for the period between January 22, 2020 till June 19, and June 20 till January 2, 2021 which marks two stages, each stage indicating the first and the second wave respectively. We discuss various forecasting approaches and the criteria for choosing the best forecasting technique. The best forecasting model selected was compared using the forecasting assessment criterion known as Mean Absolute Error (MAE). The empirical results show that the ETS and ARIMA models outperform the ANN and Hybrid models. The main finding from the ETS and ARIMA models analysis indicate that the magnitude of the increase in total confirmed cases over time is declining and the percentage change in the death rate is also on the decline. Our results shows that the chosen forecaste models are consistent during the first and second wave of of the pandemic. These forecasts are encouraging as the world struggles to contain the spread of COVID-19. This may be the result of the social distancing measures mandated by governments worldwide.

Money currency availability in Bank Indonesia can be examined by inflow and outflow of money currency. The objective of this research is to forecast the inflow and outflow of money currency in each Representative Office (RO) of BI in East Java by using a hybrid exponential smoothing based on state space approach and calendar variation model. Hybrid model is expected to generate more accurate forecast. There are two studies that will be discussed in this research. The first studies about hybrid model using simulation data that contain pattern of trends, seasonal and calendar variation. The second studies about the application of a hybrid model for forecasting the inflow and outflow of money currency in each RO of BI in East Java. The first of results indicate that exponential smoothing model can not capture the pattern calendar variation. It results RMSE values 10 times standard deviation of error. The second of results indicate that hybrid model can capture the pattern of trends, seasonal and calendar variation. It results RMSE values approaching the standard deviation of error. In the applied study, the hybrid model give more accurate forecast for five variables : the inflow of money currency in Surabaya, Malang, Jember and outflow of money currency in Surabaya and Kediri. Otherwise, the time series regression model yields better for three variables : outflow of money currency in Malang, Jember and inflow of money currency in Kediri.