Partial Autocorrelation Research Articles

Application of empirical mode decomposition, particle swarm optimization, and support vector machine methods to predict stream flows.

Modeling stream flows is vital for water resource planning and flood and drought management. In this study, the performance of hybrid models constructed by combining least square support vector machines (LSSVM), empirical model decomposition (EMD), and particle swarm optimization (PSO) methods in modeling monthly streamflow was evaluated. For establishing the models, 42years of monthly average streamflow data was used in two hydrometer stations located in the Konya Closed Basin, covering 1964 to 2005. Lagged streamflow values ​​were selected as inputs according to partial autocorrelation values ​​in establishing the models. The dataset was divided into 70% training and 30% testing. Model performances were evaluated according to mean square error, root mean square error, correlation coefficients, scatter plot, and Taylor and Violin diagrams. As a result of the analysis, it was determined that the PSO-LSSVM and EMD-LSSVM models were slightly more successful than the single LSSVM model, and the best model was obtained with the EMD-PSO-LSSVM. In addition, in estimating monthly stream flows, 1-, 9-, 10-, 11-, and 12-month lagged streamflow values were the input combination that gave the best results in semi-arid climatic regions. This result demonstrated that EMD improved the performance of both LSSVM and PSO-LSSVM models by 1% to 5% based on correlation coefficient (R) values.

Implementasi Model Autoregressive Integrated Moving Average pada Proyeksi Komoditas Ekspor Timah

The Bangka Belitung Archipelago is a potential area in the mining sector because many soils contain tin minerals and minerals that are spread evenly. Based on this phenomenon, this study uses the ARIMA model to analyze the prediction of the number of tin export commodities in the Bangka Belitung Islands Province. The time series data used in this study begins in January 2020 and ends in September 2022, with projected results ending in June 2023. Based on the analysis results, it is found that the ARIMA model (1,1,0) is the best model that can be used to project the value of tin export commodities in the Bangka Belitung Islands Province. This model was selected through the results of the correlogram test, which shows that the data is cut off at the second lag for the Autocorrelation Function (ACF) and Partial Autocorrelation Function (PACF) plots. This projection analysis was carried out after passing the stationarity test first through the Augmented Dicky Fuller (ADF) test. Through this test, it is found that the data is stationary at the first difference, and the prob value is 0.0003 with the projected result that there will be an increase in the number of exports of tin commodities with a total increase of 0.03%. The results of this analysis can certainly be part of preventive actions for the government to be able to assist the country in increasing the country’s foreign exchange through increasing export commodities.

Aeroengine gas trajectory prediction using time-series analysis auto regressive integrated moving average

PurposeThis study aims to propose the use of time series autoregressive integrated moving average (ARIMA) models to predict gas path performance in aero engines. The gas path is a critical component of an aero engine and its performance is essential for safe and efficient operation of the engine.Design/methodology/approachThe study analyzes a data set of gas path performance parameters obtained from a fleet of aero engines. The data is preprocessed and then fitted to ARIMA models to predict the future values of the gas path performance parameters. The performance of the ARIMA models is evaluated using various statistical metrics such as mean absolute error, mean squared error and root mean squared error. The results show that the ARIMA models can accurately predict the gas path performance parameters in aero engines.FindingsThe proposed methodology can be used for real-time monitoring and controlling the gas path performance parameters in aero engines, which can improve the safety and efficiency of the engines. Both the Box-Ljung test and the residual analysis were used to demonstrate that the models for both time series were adequate.Research limitations/implicationsTo determine whether or not the two series were stationary, the Augmented Dickey–Fuller unit root test was used in this study. The first-order ARIMA models were selected based on the observed autocorrelation function and partial autocorrelation function.Originality/valueFurther, the authors find that the trend of predicted values and original values are similar and the error between them is small.

Exploring the Business-Culture Relationship with Box-Jenkins ARIMA Analysis for Forecasting the Path and Future Prospects of the Popular Music Industry

Time series analysis plays a crucial role in understanding and predicting the path and future prospects of industries, including the popular music industry. This paper constructed an Box-Jenkins ARIMA (BJ-ARIMA) methodology to analyze the time series data in the popular music industry, with a focus on the relationship between business and culture. By employing the Box-Jenkins approach, BJ-ARIMA forecast future trends and make informed predictions about the development of the industry. Identification, estimation, and diagnostic testing using the BJ-ARIMA framework are the three main components of the Box-Jenkins approach. Autocorrelation and partial autocorrelation plots are analyzed in the identification phase to help choose the best BJ-ARIMA model. The estimation phase involves fitting the selected BJ-ARIMA model to the historical data, using techniques such as maximum likelihood estimation. Finally, BJ-ARIMA diagnostic checking is performed to ensure the model's adequacy and reliability. The findings of BJ-ARIMA analysis will provide a solid foundation for forecasting trends and making informed decisions in the dynamic and evolving world of the popular music industry.

Time Series Modeling and Forecasting of Drug-Related Deaths in Iran (2014-2016).

Investigating the temporal variations and forecasting the trends in drug-related deaths can help prevent health problems and develop intervention programs. The recent policy in Iran is strongly focused on deterring drug use and replacing illicit drugs with legal ones. This study aimed to investigate drug-related deaths in Iran in 2014-2016 and forecast the death toll by 2019. In this longitudinal study, Box-Jenkins time series analysis was used to forecast drug-related deaths. To this end, monthly counts of drug-related deaths were obtained from March 2014 to March 2017. After data processing, to obtain stationary time series and examine the stability assumption with the Dickey-Fuller test, the parameters of the Autoregressive Integrated Moving Averages (ARIMA) model were determined using autocorrelation function (ACF) and partial autocorrelation function (PACF) graphs. Based on Akaike statistics, ARIMA (0, 1, 1) was selected as the best-fit model. Moreover, the Dickey-Fuller test was used to confirm the stationarity of the time series of transformed observations. The forecasts were made for the next 36 months using the ARIMA (0,1,2) model and the same confidence intervals were applied to all months. The final extracted data were analyzed using R software, Minitab, and SPSS-23. According to the Iranian Ministry of Health and the Legal Medicine Organization, there were 8883 drug-related deaths in Iran from March 2014 to March 2017. According to the time series findings, this count had an upward trend and did not show any seasonal pattern. It was forecasted that the mean drug-related mortality rate in Iran would be 245.8 cases per month until 2019. This study showed a rising trend in drug-related mortality rates during the study period, and the modeling process for forecasting suggested this trend would continue until 2019 if proper interventions were not instituted.

An Overview of Forecast Analysis with ARIMA Models during the COVID-19 Pandemic: Methodology and Case Study in Brazil

This comprehensive overview focuses on the issues presented by the pandemic due to COVID-19, understanding its spread and the wide-ranging effects of government-imposed restrictions. The overview examines the utility of autoregressive integrated moving average (ARIMA) models, which are often overlooked in pandemic forecasting due to perceived limitations in handling complex and dynamic scenarios. Our work applies ARIMA models to a case study using data from Recife, the capital of Pernambuco, Brazil, collected between March and September 2020. The research provides insights into the implications and adaptability of predictive methods in the context of a global pandemic. The findings highlight the ARIMA models’ strength in generating accurate short-term forecasts, crucial for an immediate response to slow down the disease’s rapid spread. Accurate and timely predictions serve as the basis for evidence-based public health strategies and interventions, greatly assisting in pandemic management. Our model selection involves an automated process optimizing parameters by using autocorrelation and partial autocorrelation plots, as well as various precise measures. The performance of the chosen ARIMA model is confirmed when comparing its forecasts with real data reported after the forecast period. The study successfully forecasts both confirmed and recovered COVID-19 cases across the preventive plan phases in Recife. However, limitations in the model’s performance are observed as forecasts extend into the future. By the end of the study period, the model’s error substantially increased, and it failed to detect the stabilization and deceleration of cases. The research highlights challenges associated with COVID-19 data in Brazil, such as under-reporting and data recording delays. Despite these limitations, the study emphasizes the potential of ARIMA models for short-term pandemic forecasting while emphasizing the need for further research to enhance long-term predictions.

Modeling and establishing the properties of determinism of partial autocorrelation functions of double derivatives of non-linear recurrent sequences of «nested» type in the interests of implementing the third decision scheme

Modeling and establishing the properties of determinism of partial autocorrelation functions of double derivatives of non-linear recurrent sequences of «nested» type in the interests of implementing the third decision scheme

Modeling and Forecasting Unemployment Rate in Tanzania: An ARIMA Approach

Purpose: This study aims to develop a reliable forecasting approach for Tanzania's unemployment rate and provide policymakers with an effective tool for decision-making. Unemployment forecasting is vital for informed policymaking, particularly in countries like Tanzania. Methodology: This study employs a quantitative research design and adopts Box Jenkin's methodology and the ARIMA (AutoRegressive Integrated Moving Average) model for unemployment forecasting in Tanzania. The entire available dataset for the specified period is utilized, employing a non-probability sampling technique. Diagnostic tests, including ACF (AutoCorrelation Function), PACF (Partial AutoCorrelation Function), and unit root analysis, are conducted to guide the optimal model selection. Differencing addresses non-stationarity in the time series data by removing trend and seasonality effects. The optimal model selection is based on criteria such as AIC (Akaike Information Criterion), Schwartz, and Hannan-Quinn. Findings: The study finds that the ARIMA (3,1,4) model demonstrates superior performance in forecasting the unemployment rate in Tanzania. Diagnostic checks validate the adequacy of the model, revealing white noise residuals. The forecasts indicate a consistent downward trend in unemployment rates over the next nine years, suggesting potential labour market improvements in Tanzania. These findings enhance our understanding of Tanzania's unemployment dynamics and provide valuable insights for policymakers. Originality/Value: The study lies in its application of Box Jenkin's methodology and the ARIMA model to unemployment forecasting in Tanzania. By utilizing the entire available dataset and employing diagnostic tests for model selection, the study enhances the reliability of the forecasting approach. The study offers policymakers an informed decision-making tool by providing accurate forecasts and capturing underlying trends.

Hybrid intelligent deep learning model for solar radiation forecasting using optimal variational mode decomposition and evolutionary deep belief network - Online sequential extreme learning machine

Accurate prediction of solar radiation is of great significance to improve the utilization of solar energy for photovoltaic power generation on the roofs of urban buildings. Therefore, a hybrid model, namely the OVMD-PACF-ISSA-DBN-OSELM model, is being proposed in this study for solar radiation prediction. Firstly, the data is decomposed by optimal variational mode decomposition (OVMD) technology. Secondly, the partial autocorrelation function (PACF) technology selected features for components decomposed by OVMD technology. Thirdly, a deep belief network-online sequential extreme learning machine (DBN-OSELM) prediction model is constructed, and sparrow search algorithm (SSA) is utilized to optimize the model hyperparameters. Aiming at the shortcomings of SSA algorithm, Tent map and differential evolution strategy are introduced to improve the SSA algorithm. Finally, the model is used to predict each component, and the prediction results of each component are summarized to obtain the prediction results of solar radiation. To verify that the proposed method can obtain accurate prediction results, experiments are conducted using solar radiation data for January, May and October 2022, and compared with other models. Taking January as an example, compared with shallow model BP, the RMSE, MAE and R of the proposed model are increased by 66.83%, 58.65% and 5.33%, respectively. Moreover, the experiments of the proposed model in other months have excellent results. The current findings demonstrate that the suggested model is a strong contender in the arena of solar radiation prediction, and can consequently provide valuable support in enhancing the efficiency of photovoltaic equipment installed on urban building roofs.

Modeling and Forecasting Uganda’s Beef and Cattle Milk Production using the Box-Jenkins Methodology

Beef and cattle milk production play a significant role in reducing hunger, malnutrition, and rural poverty, improving rural livelihoods, creating employment opportunities, and supporting the overall development of Uganda's economy. This study was conducted to find a suitable ARIMA model for forecasting Uganda’s beef and cattle milk production using annual time series data from 1961 to 2020, extracted from the Food and Agriculture Organization Corporate Statistical Database (FAOSTAT). Following patterns of the Autocorrelation Function and Partial Autocorrelation Function plots of the differenced series, 4 tentative ARIMA models were identified for milk production, i.e., ARIMA (0,1,0), ARIMA (1,1,0), ARIMA (0,1,1), and ARIMA (1,1,1). While 3 tentative ARIMA models were identified for beef production, i.e., ARIMA (1,1,1), ARIMA (1,1,0), and ARIMA (0,1,1). ARIMA (0,1,0) model was selected to be the most suitable for forecasting cattle milk production because it had the smallest MAPE and Normalized BIC values. On the other hand, ARIMA (1,1,0) was selected to be the best model for forecasting beef production because it had the smallest normalized BIC value and a significant coefficient of the autoregressive component. Forecasts show that milk production will increase at an annual average rate of 1.63%, while beef production will increase at an annual average rate of 0.39% in the five-year forecast period (2021-2025). These findings are important in designing strategies to improve the beef and dairy livestock sub-sectors in Uganda.

An enhanced hybrid model based on multiple influencing factors and divide-conquer strategy for carbon price prediction

Accurate prediction of carbon price is of great significance for promoting the steady development of carbon trading market. However, as the unstable and nonlinear characteristics of carbon prices, it is challenging to obtain accurate future transaction prices. Therefore, this paper proposes a hybrid system for carbon price prediction. Specifically, the two-stage data preprocessing can decompose and reconstruct the carbon price sequence, which can reduce noise and chaotic disturbance and improve the quality of input data. Moreover, extreme gradient boosting (XGBoost) and partial autocorrelation function (PACF) are proposed to screen the influencing factors and carbon price subsequences to obtain the optimal features. The prediction and combination module uses the strategy of subsequence prediction and nonlinear integration, leveraging the strengths of each model to achieve the ideal results. In this system, an effective slime mold algorithm (SMA) is used to ensure the accuracy and stability of the prediction system. The research results show that: (a) The developed system has the best predictive performance compared to the benchmark models. (b) Energy, economy and commodity markets have a more significant long-term impact on carbon prices, and news sentiment and Baidu index contribute to their short-term fluctuations.

The Effects of Graded Levels of Calorie Restriction: XX. Impact of Long-Term Graded Calorie Restriction on Survival and Body Mass Dynamics in Male C57BL/6J Mice.

Calorie restriction (CR) typically promotes a reduction in body mass, which correlates with increased lifespan. We evaluated the overall changes in survival, body mass dynamics, and body composition following long-term graded CR (580 days/19 months) in male C57BL/6J mice. Control mice (0% restriction) were fed ad libitum in the dark phase only (12-hour ad libitum [12AL]). CR groups were restricted by 10%-40% of their baseline food intake (10CR, 20CR, 30CR, and 40CR). Body mass was recorded daily, and body composition was measured at 8 time points. At 728 days/24 months, all surviving mice were culled. A gradation in survival rate over the CR groups was found. The pattern of body mass loss differed over the graded CR groups. Whereas the lower CR groups rapidly resumed an energy balance with no significant loss of fat or fat-free mass, changes in the 30 and 40CR groups were attributed to higher fat-free mass loss and protection of fat mass. Day-to-day changes in body mass were less variable under CR than for the 12AL group. There was no indication that body mass was influenced by external factors. Partial autocorrelation analysis examined the relationship between daily changes in body masses. A negative correlation between mass on Day 0 and Day +1 declined with age in the 12AL but not the CR groups. A reduction in the correlation with age suggested body mass homeostasis is a marker of aging that declines at the end of life and is protected by CR.

Designing a decomposition-based multi-phase pre-processing strategy coupled with EDBi-LSTM deep learning approach for sediment load forecasting

Forecasting accurately suspended sediment load (SSL) in the basin is one of the most critical issues for river engineering, environment, and water resources management which effectively reduces flood damages. In this study, a new multi-criteria hybrid expert system comprised of empirical wavelet decomposition (EWT) integrated with Encoder-Decoder Bidirectional long short-term memory (EDBi-LSTM), supported by five feature selection (FS) methods was developed for the first time to forecast daily SSL at two study sites (Bamini and Ashti) of Godavari river basin, India. The employed FS schemes are including Boruta-Random forest (BRF), simulated annealing (SA), Relief algorithm, Ridge regression (RR), and Mutual information (MI) where the BRF coupled with EWT and EDBi-LSTM (i.e., EWT-EDBi-LSTM-Boruta) is identified as the main forecasting paradigm. Here the original SSL signals in the monsoon season (2001–2015) as the only input information were considered to forecast SSL events at a daily time scale in both study zones. The SSL signals were decomposed using the EWT technique considering the significant antecedent time-lagged inputs based on partial auto-correlation function (PACF). In the next stage, five FS strategies were addressed to specify the significant sub-sequences to reduce computational cost and enhance forecasting accuracy. Besides, the extreme gradient boosting (XGB) approach was implemented to compare the potential of the hybrid EDBi-LSTM and standalone counterpart models for both study sites. According to several goodness-of-fit indices and validation tools, the outcomes at the Bamini and Ashti sites demonstrated that the EWT-EDBi-LSTM-Boruta as the main model, achieved the best accuracy, followed by EWT-XGB-Boruta, EWT-EDBi-LSTM-SA, and EWT-XGB-SA, respectively. Comparing all the hybrid models showed that the BRF, SA, and RR strategies performed better in integration with machine learning (ML) models.

A novel combined model based on echo state network optimized by whale optimization algorithm for blast furnace gas prediction

The accurate prediction of blast furnace gas (BFG) holder level is crucial for reasonable gas dispatch. Therefore, we propose an improved echo-state network (ESN) model, based on variational modal decomposition (VMD) and whale optimization algorithm (WOA), for the BFG system. This model extracts inherent characteristic components of the sequence using VMD for prediction and determines model inputs via partial autocorrelation functions (PACF). ESN effectively handles the shortcomings of other classical neural networks with many training parameters and slow calculation speed. The important parameters are optimized through WOA to improve the prediction accuracy of the proposed model. Based on our proposed model, the average MAPE of three datasets is 0.1805% for 1-Step prediction, 0.1829% for 3-Step prediction, and 0.1886% for PACF prediction. With high prediction accuracy for BFG holder level, our model takes less time to establish and calculate, meeting requirements for short-term level prediction and more reasonable BFG scheduling decisions. The experiments and discussions support the correctness, effectiveness, and superiority of our model.

ANFIS-based soft computing models for forecasting effective drought index over an arid region of India

Abstract Drought is a natural hazard that is characterized by a low amount of precipitation in a region. In order to evaluate the drought-related issues that cause chaos for human well-being, drought indices have become increasingly important. In this study, the monthly precipitation data from 1964 to 2013 (about 50 years) of the Jodhpur district in the drought-prone Rajasthan state of India was used to derive the effective drought index (EDI). The machine learning models hybridized with evolutionary optimizers such as the genetic algorithm adaptive neuro-fuzzy inference system (GA-ANFIS) and particle swarm optimization ANFIS (PSO-ANFIS) were used in addition to the generalized regression neural network (GRNN) to predict the EDI index. Using the partial autocorrelation function (PACF), models for forecasting the monthly EDI were constructed with 2-, 3- and 5-input combinations to evaluate their outcomes based on various performance indices. The results of the different combination models were compared. With reference to 2-input and 3-input combination models, both GA-ANFIS and PSO-ANFIS show better performance results with R2 = 0.75, while among the models with 5-input combination, GA-ANFIS depicts better performance results compared to other models with R2 = 0.78. The results are presented suitably with the aid of scatter plots, Taylor's diagram and violin plots. Overall, the GA-ANFIS and PSO-ANFIS models outperformed the GRNN model.

Analysis of Stream Inflow and Peak Flow of Kainji Lake Using Stochastic Models

The research worked on flood forecasting of Kainji Lake using stochastic models by making use of average monthly inflow data for 30 years from the period of 1990 to 2021 and average annual peak flows data for 21 years from 2000 to 2021 collected from Kainji Dam meteorological station. MINITAB and SPSS software were used for the analysis. The potential models selected for the analysis were ARIMA Models of order (2,1,2) and (2,1,0) for inflows and (1,1,1) and (1,1,0) for peak flows. The selection of these models was done by identifying their features using Auto and Partial Autocorrelation functions of having the lowest values of Mean Absolute Percentage Error (MAPE), Mean Absolute Error (MAE), Sum of Squares (SS) and Mean Squares (MS) when compared to the other models. Furthermore, the analysis of the residuals for Auto and Partial Autocorrelation functions, normal probability and Histogram plots were obtained and used for the validation of the models, the results show ARIMA of order (2,12) and (1,1,1) for in-flow and peak flow were the best. Twelve and a half (12.5) and five (5) years of forecast data for the two cases were obtained. The forecast result showed that the months of August to October 2023 have high inflow values with September having the highest inflow with a value of 3471.33 (m3/sec). This highlighted the importance and usefulness of these models in warning the communities around the study area of likely impending flood events from the months of September to October and also the land around the study area can be used for agricultural purposes during the months of March to July due to low flows.

Stock Price Forecasting Based on ARIMA Model an Example of Cheung Kong Hutchison Industrial Co.

Previous studies in stock prediction mainly researched the ARIMA model, however, scant studies take Hong Kong stock price prediction as a data source for this model. The present study takes Cheung Kong Hutchison Industrial Co. as an example. With conducting descriptive analysis and the ARIMA model, this study goes through four steps: 1) Stationarity Processing: the time series data are pre-processed with differential operations to be stationary, and the series are tested for stationarity by the unit root (ADF) test. 2) Order determination: the order can be observed by drawing autocorrelation and partial autocorrelation plots. The ARIMA model's p and q values can then be calculated through SPSS. 3) Validity tests: A Q-value Table is set to determine whether the residual term conforms to the white noise distribution. Moreover, a Ljung-Box test is performed to determine whether the residual series correlated. 4) Prediction: The stock prices in the next few trading days are predicted and analyzed according to the model. The main finding of this research suggests that the price of the stock will decline at a relatively gradual pace from 48.55 to 48.51 over the next five trading days. Moreover, the ARIMA model predicts preciously this time with an error of no more than 3%. The findings can inspire researchers with the application of the ARIMA model, which can also offer suggestions for traders to obtain returns in the HK stock market.

Forecasting occurrence of palm weevil Rhynchophorus palmarum L. (Coleoptera, Curculionidae) using Autoregressive Integrated Moving Average modeling

Oil palm (Elaeis guineensis L.) is a crucial crop in Ecuador, considerably affected by black palm weevil Rhynchophorus palmarum L. (Coleoptera: Curculionidae) for several years. Despite its importance, the behavior of the black weevil in Ecuador is not well comprehended presently. Therefore, this study aimed to predict infestation patterns of the black palm weevil in Ecuador using a mathematical model based on monitoring data. Data on the number of insects per trap from a commercial oil palm farm in Quinindé, Ecuador, was collected every two weeks for five years (2016-2020) and analyzed using the Classical Fourier (CF) spectrum and the Dickey-Fuller test to determine seasonality. The trend component of the data dropped from 16.33 in January 2017 to 11.96 in January 2019, with a fluctuation ranging from -0.11 to 2.50 observed for the entire data set. The results obtained after fitting the model ranged from -0.11 to 3.19, with a maximum of 5.30. The augmented Dickey-Fuller (ADF) test for the black weevil time series yielded a result of -5.60 (P<0.01). The partial autocorrelation ranged from -0.35 to 0.1. Based on our model, we projected the occurrence of black palm weevil from 2021 to 2024, with a fluctuation in the number of insects per trap ranging from 12.68 in January 2021 to 13.023 in November 2023. This model can be used to predict future insect occurrences in Ecuador, providing valuable insights into the behavior of the black weevil and using it for effective development control measures for this pest.

Modeling and establishing the properties of determinism of partial autocorrelation functions of double derivatives of recurrent sequences of «non-nested» type in the interests of implementing the third decision scheme

Modeling and establishing the properties of determinism of partial autocorrelation functions of double derivatives of recurrent sequences of «non-nested» type in the interests of implementing the third decision scheme

Time Series Analysis for The Treatment of Typhoid (Enteric) Fever in Maiduguri: Using Arima Model

This research employs the ARIMA model to conduct a thorough time series analysis on the treatment of typhoid (enteric) fever in Maiduguri. The study reveals the presence of both trend and seasonality in the data, with the trend indicating a recent reduction in the recorded data. Using autocorrelation and partial autocorrelation function (ACF and PACF), the data can also be utilized to determine the model's order. The model obtained is subjected to model diagnostics to determine its efficiency and the model is used to forecast the typhoid fever. From the forecast graph shows that there may be a decrease in future years due to the pattern of the series the impression, we obtain from the graph is that predicted series seems to be trend upward and then downward. ARIMA (1,0,0) has the minimum value of AIC therefore it found to be best model. Hence, the model to fit the typhoid fever based on diplomatic test, which is LJung Box test from the family of Box Janks procedure, then our P-value is less than 0.05 level of significant, we reject the null hypothesis and conclude that the typhoid fever is statistically significant at 5% level of significant. Forecast of typhoid fever from February to December 2025 we also conclude that the typhoid fever is stable. Improve Sanitation and Hygiene: Implement measures to improve sanitation and hygiene practices, especially in areas with high disease prevalence. This may include promoting access to clean water, proper waste management, and hygiene education campaigns.Keyword: ARIMA Model, Typhoid fever, Box janks, WHO, Model diagnostic.