Seasonal Autoregressive Integrated Moving Average Research Articles

Exploring the substitution within clean energy: Evidence from China's top 14 hydropower provinces

This paper quantitatively examines the substitution effects within China's clean energy sector, focusing on the hydropower and new energy generation sectors across the top 14 hydropower-producing provinces, which collectively contribute to over 80 % of the country's total hydropower output. To provide a comprehensive analysis of regions that significantly influence national trends, the study utilizes the Cross-Price Elasticity (CPE) and Morishima Elasticity of Substitution (MES). CPE measures how the quantity demanded of one energy source responds to a change in the price of another, while MES assesses the sensitivity of the ratio between two energy inputs to price changes. A Seasonal Autoregressive Integrated Moving Average (SARIMA) model is employed to forecast energy substitution dynamics, offering robust predictive accuracy. The average MES between clean energy and thermal power is 0.663, indicating a moderate substitution relationship, with the effect more pronounced in summer. Additionally, the mean MES between hydropower and new energy generation is 2.067, reflecting a strong substitution effect between these two clean energy forms. Furthermore, the SARIMA model shows a mean squared error (MSE) as low as 0.0006 in some cases, demonstrating its robust predictive accuracy in forecasting energy substitution dynamics. These results offer empirical support for policies aimed at reducing reliance on thermal power and promoting clean energy development in key provinces.

Epidemiological changes of scarlet fever before, during and after the COVID-19 pandemic in Chongqing, China: a 19-year surveillance and prediction study

BackgroundThis study aimed to investigate the epidemiological changes in scarlet fever before, during and after the COVID-19 pandemic (2005–2023) and predict the incidence of the disease in 2024 and 2025 in Chongqing Municipality, Southwest China.MethodsDescriptive analysis was used to summarize the characteristics of the scarlet fever epidemic. Spatial autocorrelation analysis was utilized to explore the distribution pattern of the disease, and the seasonal autoregressive integrated moving average (SARIMA) model was constructed to predict its incidence in 2024 and 2025.ResultsBetween 2005 and 2023, 9,593 scarlet fever cases were reported in Chongqing, which resulted in an annual average incidence of 1.6694 per 100,000 people. Children aged 3–7 were the primary victims of this disease, with the highest average incidence found among children aged 6 (5.0002 per 100,000 people). Kindergarten children were the dominant infected population, accounting for as much as 54.32% of cases, followed by students (34.09%). The incidence for the male was 1.51 times greater than that for the female. The monthly distribution of the incidence showed a bimodal pattern, with one peak occurring between April and June and another in November or December. The spatial autocorrelation analysis revealed that scarlet fever cases were markedly clustered; the areas with higher incidence were mainly concentrated in Chongqing’s urban areas and its adjacent districts, and gradually spreading to remote areas after 2020. The incidence of scarlet fever increased by 106.54% and 39.33% in the post-upsurge period (2015–2019) and the dynamic zero-COVID period (2020–2022), respectively, compared to the pre-upsurge period (2005–2014) (P < 0.001). During the dynamic zero-COVID period, the incidence of scarlet fever decreased by 68.61%, 25.66%, and 10.59% (P < 0.001) in 2020, 2021, and 2022, respectively, compared to the predicted incidence. In 2023, after the dynamic zero-COVID period, the reported cases decreased to 1.5168 per 100,000 people unexpectedly instead of increasing. The cases of scarlet fever are predicted to increase in 2024 (675 cases) and 2025 (705 cases).ConclusionsChildren aged 3–7 years are the most affected population, particularly males, and kindergartens and primary schools serving as transmission hotspots. It is predicted that the high incidence of scarlet fever in Chongqing will persist in 2024 and 2025, and the outer districts (counties) beyond urban zone would bear the brunt of the impact. Therefore, imminent public health planning and resource allocation should be focused within those areas.

Similarity analyses of causative viruses for chronic obstructive pulmonary disease and asthma exacerbations

BackgroundThe representativeness of cohort studies compared to nationwide data is a major concern. This study evaluated the similarity and seasonality of causative respiratory viruses for chronic obstructive pulmonary disease (COPD) and asthma exacerbations between retrospective multicenter cohort study and nationwide data.MethodsWe compared data from the retrospective multicenter cohort study with Korean Influenza and Respiratory Surveillance System data between 2015 and 2018. Correlation, dynamic time warping (DTW), and seasonal autoregressive integrated moving average (SARIMA) analyses were performed.ResultsSpearman correlation coefficients [ρ] indicated very strong (respiratory syncytial virus [RSV] [ρ = 0.8458] and influenza virus [IFV] [ρ = 0.8272]), strong (human metapneumovirus [HMPV] [ρ = 0.7177] and parainfluenza virus [PIV] [ρ = 0.6742]), and moderate (rhinovirus [RV] [ρ = 0.5850] and human coronavirus [HCoV] [ρ = 0.5158]) correlations. DTW analyses showed moderate (PIV) and high (IFV, RSV, and HMPV) synchronicity between the two datasets, while RV and HCoV showed low synchronicity. SARIMA analyses revealed 12-month seasonality for IFV, RSV, PIV, and HMPV. The peak season was winter for RSV and IFV, spring to summer for PIV, and spring for HMPV.ConclusionsThis was the first study to report the synchronicity between a retrospective multicenter cohort study of viruses that can cause COPD or asthma exacerbations and nationwide surveillance system data.

A Hybrid Approach for the Sales Forecasting of Paracetamol Products

The pharmaceutical industry is facing challenges due to various factors such as supply chain disruptions, changing consumer behavior, and regulatory changes. Accurate demand forecasting is essential to ensure an adequate supply of drugs. The goal of this work is to forecast paracetamol product demand. For this purpose, we propose a hybrid forecasting model combining two effective forecasting techniques: SARIMA (Seasonal AutoRegressive Integrated Moving Average) and ANFIS (Adaptive Neuro-Fuzzy Inference System). This proposal consists of nonlinear components of time series by ANFIS and adjusting the result by the mean of the residuals of the SARIMA to improve the accuracy and performance of ANFIS predictions. Before the prediction phase, we preprocess our data and detect the anomalies in our dataset with Locally Selective Combination in Parallel Outlier Ensembles (LSCP). Then, by treating these anomalies as missing values, they are imputed using the combination of Fuzzy-Possibilistic c-means (FCM) with support vector regression (SVR) and a genetic algorithm (GA). Finally, we evaluate the performance of the model and some known models based on MAPE. We choose the hybrid model SARIMA-ANFIS that provides the most accurate and reliable forecasting.

Time Series Analysis to Estimate the Volume of Drinking Water Consumption in the City of Meoqui, Chihuahua, Mexico

Water is a vital resource for sustaining life and for numerous processes within the transformation industry. It is a finite resource, albeit one that can be renewed, and thus sustainable management is imperative. To achieve this objective, it is necessary to have the appropriate tools to assist with the planning policies for its management. This paper presents a time series analysis approach to measure and predict the pattern of water consumption by humans throughout subsectors (domestic, commercial, public sector, education, industry, and raw water) and total water consumption in Meoqui, Chihuahua, Mexico with data from 2011 to 2023, applying calibration model techniques to measure uncertainty in the forecasting. The municipality of Meoqui encompasses an area of 342 km2. The climate is semi-arid, with an average annual rainfall of 272 mm and average temperatures of 26.4 °C in summer and 9.7 °C in winter. The municipal seat, which has a population of 23,140, is supplied with water from ten wells, with an average consumption of 20 ± 579 m3 per user. The consumption of the general population indicates the existence of a seasonal autoregressive integrated moving average (SARIMA) (0,1,2)(0,0,2)12 model. (Sen’s Slope = 682.7, p &lt; 0.001). The domestic sector exhibited the highest overall consumption, with a total volume of 17,169,009 m3 (13 ± 93). A SARIMA (2,1,0)(2,0,0)12 model was estimated, with a Sen’s slope of 221.65 and a p-value of less than 0.001. The second-largest consumer of total water was the “raw water” sector, which consumed 5,124,795 (30,146 ± 35,841) m3 and exhibited an SARIMA (0,1,1)(2,0,0)12 model with no statistically significant trend. The resulting models will facilitate the company’s ability to define water resource management strategies in a sustainable manner, in alignment with projected consumption trends.

Development and Comparison of Time Series Models in Predicting Severe Fever with Thrombocytopenia Syndrome Cases - Hubei Province, China, 2013-2020.

Severe fever with thrombocytopenia syndrome (SFTS) is an emerging infectious disease caused by the SFTS virus, which has a high mortality rate. Predicting the number of SFTS cases is essential for early outbreak warning and can offer valuable insights for establishing prevention and control measures. In this study, data on monthly SFTS cases in Hubei Province, China, from 2013 to 2020 were collected. Various time series models based on seasonal auto-regressive integrated moving average (SARIMA), Prophet, eXtreme Gradient Boosting (XGBoost), and long short-term memory (LSTM) were developed using these historical data to predict SFTS cases. The established models were evaluated and compared using mean absolute error (MAE) and root mean squared error (RMSE). Four models were developed and performed well in predicting the trend of SFTS cases. The XGBoost model outperformed the others, yielding the closest fit to the actual case numbers and exhibiting the smallest MAE (2.54) and RMSE (2.89) in capturing the seasonal trend and predicting the monthly number of SFTS cases in Hubei Province. The developed XGBoost model represents a promising and valuable tool for SFTS prediction and early warning in Hubei Province, China.

Pollutants-mediated viral hepatitis in different types: assessment of different algorithms and time series models

The escalating frequency of environmental pollution incidents has raised significant concerns regarding the potential health impacts of pollutant fluctuations. Consequently, a comprehensive study on the role of pollutants in the prevalence of viral hepatitis is indispensable for the advancement of innovative prevention strategies. Monthly incidence rates of viral hepatitis from 2005 to 2020 were sourced from the Chinese Center for Disease Control and Prevention Infectious Disease Surveillance Information System. Pollution data spanning 2014–2020 were obtained from the National Oceanic and Atmospheric Administration (NOAA), encompassing pollutants such as CO, NO2, and O3. Time series analysis models, including seasonal auto-regressive integrated moving average (SARIMA), Holt-Winters model, and Generalized Additive Model (GAM), were employed to explore prediction and synergistic effects related to viral hepatitis. Spearman correlation analysis was utilized to identify pollutants suitable for inclusion in these models. Concurrently, machine learning (ML) algorithms were leveraged to refine the prediction of environmental pollutant levels. Finally, a weighted quantile sum (WQS) regression framework was developed to evaluate the singular and combined impacts of pollutants on viral hepatitis cases across different demographics, age groups, and environmental strata. The incidence of viral hepatitis in Beijing exhibited a declining trend, primarily characterized by HBV and HCV types. In predicting hepatitis prevalence trends, the Holt-Winters additive seasonal model outperformed the SARIMA multiplicative model ((1,1,0) (2,1,0) [12]). In the prediction of environmental pollutants, the SVM model demonstrated superior performance over the GPR model, particularly with Polynomial and Besseldot kernel functions. The combined pollutant risk effect on viral hepatitis was quantified as βWQS (95% CI) = 0.066 (0.018, 0.114). Among different groups, PM2.5 emerged as the most sensitive risk factor, notably impacting patients with HCV and HEV, as well as individuals aged 35–64. CO predominantly affected HAV patients, showing a risk effect of βWQS (95% CI) = − 0.0355 (− 0.0695, − 0.0016). Lower levels of PM2.5 and PM10 were associated with heightened risk of viral hepatitis incidence with a lag of five months, whereas elevated levels of PM2.5 (100–120 μg/m3) and CO correlated with increased hepatitis incidence risk with a lag of six months. The Holt-Winters model outperformed the SARIMA model in predicting the incidence of viral hepatitis. Among machine learning algorithms, SVM and GPR models demonstrated superior performance for analyzing pollutant data. Patients infected with HAV and HEV were primarily influenced by PM10 and CO, whereas SO2 and PM2.5 significantly impacted others. Individuals aged 35–64 years appeared particularly susceptible to these pollutants. Mixed pollutant exposures were found to affect the development of viral hepatitis with a notable lag of 5–6 months. These findings underscore the importance of long-term monitoring of pollutants in relation to viral hepatitis incidence.

The impact of climate variation on the spread of Shiga toxin-producing E. coli.

Shiga toxin-producing Escherichia coli (STEC) is influenced by seasonality, but there is limited understanding of how specific climatic variables contribute to disease spread. This information aids in understanding disease transmission dynamics and could potentially inform public health modeling. This retrospective cohort study analyzed public health data from Ontario, Canada, between 2012 and 2021, along with historical climate data from Environment Canada. We employed Seasonal Autoregressive Integrated Moving Average (S-ARIMA) models to assess how temperature and precipitation impact the incidence of STEC infections, measured per 10,000,000 population. The study included 1658 confirmed STEC cases. A significant correlation was found between STEC incidence and climatic variables. Each degree Celsius increase in maximum temperature was associated with a rise of 3 STEC cases per 10,000,000 population (Centers for Disease Control and Prevention (2024)). Additionally, each millimeter of increased precipitation correlated with an increase of 1.1 cases per 10,000,000 population. The findings demonstrate a significant impact of temperature and precipitation on STEC transmission, highlighting the importance of integrating meteorological data into public health surveillance. This integration may help inform public health responses and support healthcare systems in planning for future outbreaks. Further studies are needed to refine predictive models and develop effective early warning systems for clinical settings.

Forecasting of Electricity Consumption by Seasonal Autoregressive Integrated Moving Average Model in Assam, India

Sustainable electricity consumption, which is about balancing economic growth, social development and environmental protection are the core principles of the Sustainable Development Goal (SDG). Accurate forecasting of electricity consumption is very important for attaining SDG - 7 which aims to ensure access to affordable, reliable, sustainable and modern energy for all. Through this paper, attempt is made to forecast monthly electricity consumption in Assam. For this purpose, one of the most widely used time series techniques, viz., Seasonal Autoregressive Integrated Moving Average (SARIMA) is applied by considering the time period April, 2013 to February, 2023 to study the seasonal influence on the electricity consumption in Assam. By applying Augmented Dickey Fuller test, it is observed that the data series becomes stationary at first order difference and the result of Canova Hansen test reveals that no seasonal differencing is required for our considering time period. SARIMA (1,1,1) (1,0,1)12 has been selected for forecasting purpose by following the results of Akaike Information Criterion. By analyzing the model statistics, residual ACF and PACF plots of the selected model, it is found that SARIMA (1,1,1) (1,0,1)12 can be effectively recommended for forecasting of monthly electricity consumption in Assam with Mean Absolute Percentage Error as 3.12%.

A Consensus-based Traffic Prediction for Time Series Data in SDN

Objective: This research proposes a methodology for improving real-time traffic prediction by constructing dataset from the live traffic in Software-Defined Networks (SDNs). Methods: This work applies time-series based machine learning models such as XGBoost Regressor, LSTM, and Seasonal ARIMA, on the collected and preprocessed traffic data from SDN switches. Findings: Simulation shows that the percentage of error parameters that depict accuracy and goodness of fit for traffic predictions are still weak and needs improvement, as these predictions have the potential to compose new policies for the dynamic environment. Novelty: The consensus method is applied to forecast future network traffic across multiple time slots as consensus strengthens the decisions. Keywords: Software defined networking, Traffic prediction, Consensus, Machine learning, Time series data

Minitab 20 and Python based-the forecasting of demand and optimal inventory of liquid aluminum sulfate supplies

In a company, inventory management is crucial due to the significant impact on various aspects of the business. Similarly, the Indonesian water supply company (PDAM) requires effective inventory management to ensure the supply of liquid aluminum sulfate chemicals. The probabilistic statistical inventory control (SIC) model is commonly used for inventory management. However, previous research on chemical inventory models in PDAMs often relied on simple linear regression to forecast demand data, which fails to capture the inherent volatility in demand. Therefore, this research aimed to predict demand data using the seasonal autoregressive integrated moving average (SARIMA) method and determine the optimal policy for supplying liquid aluminum sulfate chemicals. The results showed that the best demand forecasting model was SARIMA (2,1,2) (1,1,0)12 with a mean absolute percentage error (MAPE) value of 8.19%. The finding of the optimal inventory policy showed a safety stock value of 11,922.35 kg, a reorder point value of 49,511.20 kg, and an order quantity of 21,526.59 kg, leading to a total cost of IDR 11,132,034,145.45. The sensitivity test also showed that variations in lead time, price, μ, and σ parameters directly influence changes in total cost, reorder point, and safety stock. These calculations were conducted using Minitab and Python software.

Forecasting Tourist Arrivals in Nepal: A Comparative Analysis of Seasonal Models and Implications

Tourist arrivals play a vital role in the broader tourism ecosystem, substantially contributing to the economy. The global landscape has witnessed significant growth in international arrivals over the years, and Nepal has not been an exception to this trend, experiencing a steady influx of inbound tourists. Although tourist numbers are increasing, the lack of research in forecasting future arrivals is evident, highlighting the pressing need for comprehensive forecasting mechanisms to efficiently manage tourism resources and sustainably accommodate the growing influx of visitors. In order to gain insights into the dynamics of international tourist arrivals in Nepal, we conducted a comparative analysis using two distinct forecasting techniques: Seasonal Autoregressive Integrated Moving Average (SARIMA) and the Exponential Smoothing technique. Our analysis spanned from January 1992 to December 2023, enabling us to formulate forecasts for the upcoming months up to December 2030. The findings of our study underscore the suitability of all three models—namely, SARIMA, Winter Additive, and Winter Multiplicative—as effective tools for projecting international arrivals in Nepal. However, upon careful examination, the Winter Multiplicative model emerged as the most appropriate model for forecasting Nepal's international arrivals. This model aligned strongly with the observed data, enhancing its predictive accuracy. The implications of our research are far-reaching, offering valuable insights for various stakeholders within Nepal's tourism industry. These insights can guide tourism planners, policymakers, and other relevant entities in formulating well-informed strategies to strengthen and sustain the growth of the tourism sector in Nepal. As the nation continues to position itself on the global tourism map, equipped with data-driven forecasts, we believe that our study provides an essential resource for shaping the trajectory of Nepal's tourism industry in a positive direction.

Fuzzified input data tuning for agriculture commodities price prediction

&lt;span lang="EN-US"&gt;The quality of the input data will typically affect the prediction accuracy. Preprocessing of data is commonly referred to as input data tuning. Tuning the input data is critical for projecting commodity prices. Anomalies or outliers are unavoidable in historical price data. To increase prediction and forecasting accuracy, it is necessary to find and correct outliers before training the prediction model. To correct the anomaly and increase prediction accuracy, the Fuzzified Input Data Tuning and Prediction algorithm proposed in this study. The identified outliers are corrected using the relevant fuzzy set value in this method. With outlier corrected data, we used Long Short-Term Memory and Seasonal Autoregressive Integrated Moving Average to anticipate tomato prices in Karnataka state. The result of the proposed algorithm is compared with the Sliding Window anomalies correction model, and without disposing of the outliers. The suggested algorithm, with 37.89%, performed better than Sliding Window with 40.08% and 43.11% Mean Absolute Percentage Error, respectively, and without outlier correction. The sensitivity analysis shows that the performance of the model is unaffected by the forecasting horizon. Finally, comparitive analysis peformed with previous research work, and the proposed model performed better.&lt;/span&gt;

Epidemiological characterization of hand, foot, and mouth disease among hospitalized children from 2014 to 2023 in a hospital in Henan Province: Longitudinal surveillance study.

Hand, foot, and mouth disease (HFMD) is an acute infectious illness primarily caused by enteroviruses. The present study aimed to describe the epidemiological characteristics of hospitalized HFMD patients in a hospital in Henan Province (Zhengzhou, China), and to predict the future epidemiological parameters. In this study, we conducted a retrospective analysis of general demographic and clinical data on hospitalized children who were diagnosed with HFMD from 2014 to 2023. We used wavelet analysis to determine the periodicity of the disease. We also conducted an analysis of the impact of the COVID-19 epidemic on the detection ratio of severe illness. Additionally, we employed a Seasonal Difference Autoregressive Moving Average (SARIMA) model to forecast characteristics of future newly hospitalized HFMD children. A total of 19 487 HFMD cases were included in the dataset. Among these cases, 1515 (7.8%) were classified as severe. The peak incidence of HFMD typically fell between May and July, exhibiting pronounced seasonality. The emergence of COVID-19 pandemic changed the ratio of severe illness. In addition, the best-fitted seasonal ARIMA model was identified as (2,0,2)(1,0,1)12. The incidence of severe cases decreased significantly following the introduction of the vaccine to the market (χ2 = 109.9, p < 0.05). The number of hospitalized HFMD cases in Henan Province exhibited a seasonal and declining trend from 2014 to 2023. Non-pharmacological interventions implemented during the COVID-19 pandemic have led to a reduction in the incidence of severe illness.

Time series analysis of sea surface temperature change in the coastal seas of Türkiye

Sea surface temperature (SST) is a crucial geophysical parameter in assessing heat exchange between the air and sea surface. Changes in SST and its accurate prediction play a pivotal role in explaining the global heat balance, determining atmospheric circulations, and constructing global climate models. This work aims to reveal a model for one-month-ahead forecasting of SST time series data along the Türkiye coasts, encompassing the Mediterranean, Aegean, Marmara, and Black Seas, and their long-term future forecast. A long short-term memory (LSTM) neural network and seasonal autoregressive integrated moving average (SARIMA) models are used for this purpose. The ECMWF ERA5 (0.5ox0.5°) monthly SST dataset spanning the years 1970–2023 is used for model development. The results obtained from the LSTM and SARIMA models show that there will be an increasing trend in SSTs along these seacoasts until 2050. The SST measurements of 23.4 °C, 20.2 °C, 17.0 °C, and 16.6 °C recorded along the Mediterranean, Aegean, Marmara, and Black Seas in 2023 are expected to rise to 25.1 °C, 21.9 °C, 18.1 °C, and 18.8 °C, respectively, by 2050. These figures indicate an increase of 7.3%, 8.4%, 6.5%, and 13.3% in the SST values across these coastal seas over the next quarter century.

Forecasting of Inland Fish Production: Case of Catla (&lt;em&gt;Catla catla&lt;/em&gt;) and Gift Tilapia (&lt;em&gt;Oreochromis niloticus&lt;/em&gt;) Production in Udawalawa Reservoir in Sabaragamuwa Province, Sri Lanka

This study focused on assessing and forecasting Catla (Catla catla) and Tilapia (Oreochromis niloticus) production in the Udawalawe reservoir in Sri Lanka using an 11-year time series data from 2010 to 2021. The relevant secondary data were collected from the National Aquaculture Development Authority of Sri Lanka (NAQDA). Unit root tests, Dickey-Fuller tests, and Seasonal Auto Regressive Integrated Moving Average (SARIMA) models and trend analysis were applied for the data analyses. According to the results, stationarity behaviour was observed in both Catla and Tilapia production information series. Hence, SARIMA (2,2,1) (1,0,1)12 is the appropriate empirical model for forecasting Catla production. Furthermore, the maximum average landings of Catla production were observed in the March-June time period. SARIMA (1,0,1) (1,1,1)12 was indicated as the most suitable model to forecast Tilapia production in the reservoir. The maximum average of Tilapia production was also observed in the March-June period. Both the SARIMA model and trend analysis gave approximately equal production information regarding Catla and Tilapia. Thus, these findings showed that the SARIMA model has more accuracy than trend analysis when analysing the time series information for short durations. However, when the duration becomes larger, forecasting is not suitable using the SARIMA model, and trend analysis gives a clear view up to a certain level. Both Catla and Tilapia production exhibited significant changing patterns and multiple seasonalities. Thus, trend analysis gives valuable insights than SARIMA model in long term predictions in case of this study. These findings are highly important for enhancing fish production in this reservoir, as they predict future fish catches under the current reservoir conditions.

Modelling Petrol Prices in Kenya from 2014 to 2023 Using Sarimax Model: A Case Study of Nairobi County

The requirement for petrol price information is crucial for majority of enterprises. This is because fluctuations in petrol prices impact inflation hence affecting daily lives of citizens. In analyzing the prices of petrol, researchers have employed several models but encountered various limitations. These limitations include; the Error Correction Model can examine only one co-integrating association. The Vector Autoregression (VAR) model does not account for the structural changes in the data. Additionally, the AutoRegressive Integrated Moving Average (ARIMA) model does not take into consideration the seasonal component in the data. The Generalized Autoregressive Conditional Heteroskedasticity (GARCH) model assumes that over time the volatility is constant. Moreover, the Seasonal Autoregressive Integrated Moving Average (SARIMA) model does not integrate the external factors. Hence in this study Seasonal Autoregressive Integrated Moving Average with Exogenous Variables (SARIMAX) model was employed since it captures seasonality in data and incorporates the exogenous variables. The research’s aim was to model prices of petrol in Kenya for the period between 2014 to 2023 with exchange rates as an external factor. Secondary data was obtained from Energy and Petroleum Regulatory Authority (EPRA), Kenya National Bureau of Statistics (KNBS) and Central Bank of Kenya (CBK) websites. R software was used to analyze the data. By the use of historical data of petrol prices and exchange rates, the study sought to fit the best Seasonal Autoregressive Integrated Moving Average with Exogenous Variables (SARIMAX) model, validate the model and predict the petrol prices. The petrol price data was found to be non-stationary using Augmented Dickey Fuller test (ADF). Regular differencing was conducted to make the data stationary. Seasonal differencing due to seasonality component available in the data was also performed. Best SARIMAX model was chosen from various SARIMAX models according to Box-Jenkins methodology which uses least Akaike Information Criterion (AIC) value. SARIMAX (0,1,1)(2,1,2)&amp;lt;sub&amp;gt;12&amp;lt;/sub&amp;gt; model was selected since it had least Akaike Information Criterion (AIC) value of 656.3733 and the model validated using the hold out technique. The forecasts errors from the training set were; Mean Squared Error (MSE)=10.4970, Root Mean Square Error (RMSE)=3.239911, Mean Absolute Percentage Error (MAPE)=2.309268% while those from the testing set were; Mean Squared Error (MSE)=3271.1012, Root Mean Square Error (RMSE)=57.193542, Mean Absolute Percentage Error (MAPE)=26.695390%. There was less error in the training set than in the testing set as it was expected hence the model suited the data well and could be used for future predictions. The model was then used for five year forecast into the future. This study’s findings will offer sound suggestions to policymakers, businesses and consumers. This study recommends a model to be fitted using other factors affecting petrol prices and fitting Fourier terms, Behavioral Assessment Tools (BATS) and Trigonometric Box-Cox ARMA Trend Seasonal (TBATS) models.

A hybrid SARIMA-Prophet model for predicting historical streamflow time-series of the Sobat River in South Sudan

Accurate river streamflow forecasting is pivotal for effective water resource planning, infrastructure design, utilization, optimization, and flood planning and warning. Streamflow prediction remains a difficult task due to several factors such as climate change, topography, and lack of observed data in some cases. This paper investigates and evaluates the individual performances of the seasonal auto-regressive integrated moving average (SARIMA) and Prophet models in forecasting the streamflow of the Sobat River and proposes a hybrid SARIMA-Prophet model to leverage the strengths of both approaches. Using the augmented Dickey-Fuller (ADF) and the Kwiatkowski-Phillips-Schmidt-Shin (KPSS) tests, the flow of the Sobat River was found to be stationary. The performance of the models was then assessed based on their residual errors and predictive accuracy using the mean absolute error (MAE), root mean squared error (RMSE), and coefficient of determination (R2). Residual analysis and prediction capabilities revealed that Prophet slightly edged SARIMA in terms of prediction efficacy; however, both models struggled to effectively capture extreme values, resulting in significant overestimations and slight underestimations. The hybrid SARIMA-Prophet model significantly reduced residual variability, achieving a lower MAE of 4.047 m3/s, RMSE of 6.17 m3/s, and a higher R2 of 0.92 than did the SARIMA (MAE: 5.39 m3/s, RMSE: 8.70 m3/s, R2: 0.85) and Prophet (MAE: 5.35 m3/s, RMSE: 8.32 m3/s, and R2: 0.86) models. This indicates that the hybrid model handles both long-term patterns and short-term fluctuations more effectively than the individual models. The findings of the present study highlight the potential of hybrid SARIMA-Prophet models for streamflow forecasting in terms of accuracy and reliability, thus contributing to more effective water resource management and planning, particularly in the Sobat River.

Application of Vector Autoregressive (VAR) Model on the Interaction of Inflation Rates and Public Debt in Kenya from 2011 to 2021

This study examines the relationship between public debt and inflation rates in Kenya from 2011 to 2021 using the Vector Autoregressive (VAR) model. Despite the models likeAutoregressive Integrated Moving Average (ARIMA), Seasonal Autoregressive Integrated Moving Average (SARIMA), and Generalized Autoregressive Conditional Heteroscedasticity (GARCH) gaining popularity in time series analysis, the Vector Autoregressive model, being multivariate, is relevant in analyzing two or more time series variables simultaneously, benefiting from the bi-directional causality and providing a better outlook into the flow of the dynamic interaction between inflation and public debt. The main objectives are modelling the Vector Autoregressive model and forecasting future trends to provide insights for policymakers. Additionally, the methodological approach comprises descriptive statistics, stationarity tests, normality tests, and the Vector Autoregressive model. Descriptive statistics reveal significant variations, with public debt increasing from 1.35 trillion KES to a peak of 8.2 trillion KES, and inflation rates ranging from 3.2% to 19.72% for the period from 2011 to 2021. The Augmented Dickey-Fuller (ADF) test confirmed that both time series were stationary at their levels. The Vector Autoregressive model, chosen for its ability to analyze dynamic interactions, indicated a significant relationship between the variables, with inflation showing strong self-persistence (coefficient of 0.8731, &amp;lt;i&amp;gt;p&amp;lt;/i&amp;gt; &amp;lt; 2 × 10&amp;lt;sup&amp;gt;−16&amp;lt;/sup&amp;gt;), though public debt did not significantly impact inflation in the model (&amp;lt;i&amp;gt;p&amp;lt;/i&amp;gt; = 0.5592). The models R-squared values, 95.82% for public debt and 84.74% for inflation, highlight its strong explanatory power. Moreover, findings indicate that while public debt does not directly affect inflation within the model lag structure, inflation exhibits a strong self-persistence. The model R-squared values are 95.82% for public debt and 84.74% for inflation, demonstrating high explanatory power. Recommendations include the implementation of a robust debt management strategy, emphasizing sustainable borrowing and enhancing revenue generation to mitigate inflationary pressures. Further research is recommended to explore the broader macroeconomic impacts of public debt on economic growth and employment in Kenya.

Predicting the incidence of rifampicin resistant tuberculosis in Yunnan, China: a seasonal time series analysis based on routine surveillance data

BackgroundRifampicin resistant tuberculosis (RR-TB) poses a growing threat to individuals and communities. This study utilized a seasonal autoregressive integrated moving average (SARIMA) model to quantitatively predict the monthly incidence of RR-TB in Yunnan Province which could guide government health administration departments and the centers for disease control and prevention (CDC) in preventing and controlling the RR-TB epidemic.MethodsThe study utilized routine surveillance reporting data from the infectious Disease Network Surveillance and Reporting System. Monthly incidence rates of RR-TB were collected from January 2019 to December 2022. A time series SARIMA model was used to predict the number of monthly RR-TB cases in Yunnan Province in 2023, and the model was validated using time series plots, seasonal and non-seasonal differencing, autocorrelation and partial autocorrelation analysis, and white noise tests.ResultsFrom 2019 to 2022, the incidence of RR-TB decreases as the incidence of all TB decreases (P < 0.05). There was no significant change in the proportion of RR-TB among all TB cases, which remained within 2.5% (P>0.05). The time series decomposition shows that it presented obvious seasonality, periodicity and randomness after being decomposed. Time series analysis was performed on the original series after 1 non-seasonal difference and 1 seasonal difference, the ADF test showed P < 0.05. According to ACF and PACF, the SARIMA (1, 1, 1) (1, 1, 0)12 model was chosen and statistically significant model parameter estimates (P < 0.05). The predicted seasonal trend of RR-TB incidence in 2019 to 2023 was similar to the actual data. The percentage accuracy in the prediction excesses 80% in 2019 to 2022 and is all within 95% CI. However there was a certain gap between the actual incidence and the predicted value in 2023, and the acutual incidence had increased by 12.4% compared to 2022. The percentage of accuracy in the prediction was only 70% in 2023.ConclusionsWe found the incidence of RR-TB was based on that of all TB in Yunnan. The SARIMA model successfully predicted the seasonal incidence trend of RR-TB in Yunnan Province in 2019 to 2023, but the prediction precision could be influenced by factors such as new infectious disease outbreaks or pandemics, social issues, environmental challenges or other unknown risks. Hence CDCs should pay special attention to the post epidemic effects of new infectious disease outbreaks or pandemics, carry out monitoring and early warning, and better optimize disease prediction models.