ARIMA Research Articles

Comparing ARFIMA and ARIMA Models in Forecasting under Five Mortality Rate in Tanzania

Tanzania has been taking various measures to drop the Under-Five Mortality Rate (UFMR), but the pace to meet national and global UFMR targets has been slow. Nevertheless, the decline for the past years has continued to be low as compared to the Sustainable Development Goals (SDGs) target which is set at 25 deaths/1000 live births by 2030. The lack of statistical modeling-based forecast values of UFMR results into setting targets that are not SMART towards the realization of national and international goals of the health sector. Thus, the current study uses both ARFIMA and ARIMA to make forecasts of UFMR in Tanzania from 2021 to 2030 by using data extracted from the World Databank - World Development Indicators (WDI). Also, an accuracy comparison between the ARFIMA and ARIMA best-fit models in forecasting UFMR was conducted. The forecasts from the best ARFIMA (1, 0.284243, 2) model indicate that by June 2026 the rate will on average be 41 deaths/1,000 live births as compared to the Tanzanian Five Year Development Plan Phase III (TFYDP-III) target of 40 deaths/1,000 live births; whereas the best fit ARIMA (1, 2, 0) model forecasts depict that the rate will be 40.1 deaths/1,000 live births as compared to the TFYDP-III target. In relation to the UN SDGs target of 25 deaths/1,000 live births by 2030, the ARFIMA (1, 0.284243, 2) model forecast values indicate that by 2030, Tanzania will experience a decrease in UFMR to 35.2 deaths/1,000 live births. The ARIMA (1, 2, 0) forecast values indicate that by 2030, Tanzania will experience a decrease in UFMR to 32.9 deaths/1,000 live births. The results of using RMSE and MAPE forecasting model accuracy measures reveal that the ARFIMA (1, 0.284243, 2) model performs better than ARIMA (1, 2, 0) in forecasting UFMR.

An Investigation of Exchange Rate Volatility using Econometric Model: Evidence from Cambodia

The examination of foreign exchange dynamics was performed utilizing the Autoregressive Integrated Moving Average (ARIMA) model, which integrates both Autoregressive (AR) and Moving Average (MA) components. The analysis focused on the monthly exchange rate between the Khmer Riel and the US dollar, spanning from December 2018 to September 2024, to assess the variations in exchange rates. According to the results of the Augmented Dickey-Fuller (ADF) test, the foreign exchange data series was determined to be integrated of order zero, or I(0). The model identified as the most appropriate, based on the Akaike Information Criterion (AIC), was the ARIMA(3,0,3) model, which indicated the optimal lag lengths for this analysis. The reaction of the foreign exchange market to the disturbance shock revealed a cyclical behavior and demonstrated a downward trajectory over the 30-period forecast horizon. Importantly, the impulse response function (IRF) stayed within the 95% confidence interval, signifying that the response to the shock was statistically significant and remained within a tolerable level of uncertainty. This observation implies that the predictions generated by the model can be regarded as trustworthy.

Analyzing robust dividend payout policy with dynamic panel regression: Application of speed of adjustment to half-life

This study aims to observe the effects of financial metrics, free float shareholders, GDP growth and firm age on dividend payout policy in both the short- and long-term scenarios. The study introduces the dynamic panel regression models, i.e. Autoregressive Integrated Moving Average (ARIMA) for time series data and Weighted Least Squares (WLS) to account for autocorrelation and heteroscedasticity limitation. The dataset includes all companies listed on the Stock Exchange of Thailand during the years 2013–2023. The study finds that in the long-term, GDP growth negatively relates to dividend payout policy in all industrial sectors. Financial metrics, free float shareholders, GDP growth and firm age affect a mixed picture of industrial sectors on dividend payout policy. In the short-term, previous dividend payments significantly influence dividend payment policy. Furthermore, a higher debt-to-equity ratio, firm age, and free cashflows influence dividend payout policy in various industrial sectors. Also shown by the analysis is that factors influence short-run adjustment to half-life analysis.

Trends and Disparities in Parkinson’s Disease Mortality in the United States with Predictions Using Machine Learning

Background: Parkinson’s disease (PD) is a progressive neurodegenerative condition characterized by the degradation of dopaminergic pathways in the brain. As the population in the United States continues to age, it is essential to understand the trends in mortality related to PD. This analysis of PD’s mortality characterizes temporal shifts, examines demographic and regional differences, and provides machine-learning predictions. Methods: PD-related deaths in the United States were gathered from CDC WONDER. Age-adjusted mortality rates (AAMR) were collected, and trends were analyzed based on gender, race, region, age, and place of death. Annual percent change and average annual percent change were calculated using Joinpoint Regression program. Forecasts were obtained using the optimal Autoregressive Integrated Moving Average (ARIMA) model. Results: Overall mortality rate due to Parkinson’s increased from 1999 to 2022. Male gender, White race, Southern region, and older ages were associated with higher mortality compared to other groups. Deaths at home decreased and hospice deaths increased during the study period. Conclusions: This study highlights the increasing rate of PD AAMR and how it may become even more prevalent with time, emphasizing the value of increasing knowledge surrounding the disease and its trends to better prepare health systems and individual families for the burden of PD.

Temporal, Spatial Characteristics and Prediction of Precipitation in Guangzhou Based on the SARIMA Model

This article obtains nearly 18 years of precipitation data for Guangzhou from the National Centers for Environmental Information (NCEI) under the National Oceanic and Atmospheric Administration (NOAA) and conducts visualization analysis and modeling predictions using R software.Using the classic SARIMA model (the ARIMA model with seasonal components) as well as regression and residual ARIMA models to build and simulate the precipitation series.We also used Basic-bootstrap prediction, which involves resampling the residuals of the fitted model with replacement, using historical values to predict the future and obtain a model parameter, as well as Full-bootstrap prediction (which assumes that the residuals have uncertainty and that the estimated model coefficients themselves also have uncertainty).Therefore, not only are reasonable model residuals obtained through the bootstrap method, but multiple model parameters are also derived from this method to determine more reasonable model parameters, which are then used to forecast the next 12 periods for the fitted model. Comparing the results of the four prediction models, the Full-bootstrap model under the regression model showed the best predictive performance. The study found that there is no significant trend in precipitation changes over time, but short-term fluctuations still exist. Although some extreme values appeared, they remain within a predictable range.Therefore, the relevant city government departments prone to extreme rainfall can make reasonable adjustments to drainage facilities based on local precipitation forecasts

Construction and application of optimized model for mine water inflow prediction based on neural network and ARIMA model

Mine water influx is a significant geological hazard during mine development, influenced by various factors such as geological conditions, hydrology, climate, and mining techniques. This phenomenon is characterized by non-linearity and high complexity, leading to frequent water accidents in coal mines. These accidents not only impact coal production quality but also jeopardize the safety of mine staff. In order to better predict the amount of water surging in mines and to provide an important basis for mine water damage prevention work, based on the time series data of mine water influx from January 2020 to February 2023 in Northern Guizhou Province Longfeng Coal Mine, the BP-ARIMA prediction model was established by combining the BP neural network model and ARIMA autoregressive sliding average model, It also predicted the mine influx for a total of 6 months from July 2022 to February 2023, and compared the prediction results with four models, namely, BP neural network model, ARIMA autoregressive sliding average model, traditional method of Large well method, and GM(1,1) grey model, and used the absolute relative error as the calculation of model accuracy. The results show that the established BP-ARIMA(3,1,1) prediction model is much closer to the actual value, with an average absolute relative error of 1.02% and a maximum absolute relative error of 3.036%, and the goodness of fit R² was 0.93, which is much better than the other four single models, and substantially improves the prediction accuracy of mine water influx. Furthermore, utilizing the BP-ARIMA model, future predictions for mine water influx in Longfeng Mine were made, offering a scientific foundation for effective prevention and control measures.

Trends, seasonal variations and forecasting of chronic respiratory disease morbidity in charcoal producing areas, northwest Ethiopia: time series analysis

ObjectiveThis study analyzed the trend, seasonal variations and forecasting of chronic respiratory disease morbidity in charcoal producing areas, northwest Ethiopia, aiming to provide evidences in planning, designing strategies, and decision-makings for preparedness and resource allocation to prevent CRD and reduce public health burden in the future.Materials and methodsThe trend, seasonal variation, and forecasting for CRD were estimated using data collected from the three zones of Amhara region annual reports of DHIS2 records. Smoothing decomposition analysis was employed to demonstrate the trend and seasonal component of CRD. The ARIMA (2, 1, 2) (0, 0, 0) model was used to forecast CRD morbidity. The model's fitness was checked based on Bayesian information criteria. The stationarity of the data was assessed with a line chart and statistically with the Ljung-Box Q-test. SPSS version 27 was utilized for statistical analysis.ResultsThe annual morbidity rate of CRD has shown an increasing trend in both sexes over a seven-year period among people aged 15 years and older. Seasonal variation in CRD morbidity was observed. The smoothing decomposition analysis depicted that the seasonal component was attributed to 44.47% and 19.16% of excess CRD cases in the period between September to November, and June to August, respectively. A substantial difference among the three zones of the Amhara region in CRD morbidity rate was noted, with the highest observed in the Awi zone. Forecasting with the ARIMA model revealed that CRD-related morbidity will continue to increase from 2020 to 2030.ConclusionThe study revealed that the CRD morbidity rate has shown an increasing trend from 2013 to 2019. Seasonal variation in the CRD morbidity rate was observed, with the highest peak from September to November. The morbidity attributed to CRD will continue to increase for the next ten years (2020–2030). Therefore, this study could potentially play a groundbreaking role. Further study is warranted to understand the risk factors and facility readiness through a further understanding of seasonality and future trends.

Global burden of cardiovascular diseases attributable to diet low in vegetables from 1990 to 2021 and forecasting the future trends: a population-based study

BackgroundThis investigation examines the worldwide impact of cardiovascular diseases (CVD) resulting from inadequate vegetable consumption, based on the 2021 Global Burden of Disease Study data.MethodThe study assessed the global, regional, and national repercussions of low vegetable intake on CVD, with a focus on variations among different age and gender demographics. It further analyzed the correlation between disease burden and the Socio-Demographic Index (SDI), and employed an ARIMA model to predict future trends in CVD associated with insufficient vegetable consumption up to 2050.ResultIn 2021, a diet lacking in vegetables was responsible for roughly 682,400 deaths and 16 million disability-adjusted life years (DALYs) attributed to CVD, indicating a declining pattern over recent year. Individuals aged 75 and older were predominantly affected. Future projections indicate an expected rise in CVD incidence in lower-middle SDI regions, with African nations potentially experiencing increased challenges related to low vegetable consumption by 2030 and 2050.ConclusionThe findings underscore the critical necessity for preventive measures against CVD and emphasize the significance of improving dietary habits, particularly vegetable intake.

Time series analysis of dengue incidence in Bandung City, Indonesia using a ARIMA model

Background. Dengue is a public health problem that leads to death. This disease is necessary to monitor to reduce its impact on the community. Purpose. This study aims to forecast the incidence of dengue in Bandung City using historical data from 2014 to 2023. Method. This retrospective observational study examined dengue incidence in Bandung City from 2014 to 2023, secondary data were processed and analysed using Autoregressive Integrated Moving Average (ARIMA) model to forecast dengue incidence. Results. The best model generated is ARIMA (3,0,3), Mean Absolute Percentage Error (MAPE = 33,3437) and Akaike Information Criterion (AIC = 0,1489). Based on the model, the peak of dengue cases is estimated to occur in September 2024 (320 cases). Conclusion. The peak incidence of dengue in Bandung City will occur in September 2024. Hence the need for vector control efforts in several sub-districts and increasing efforts to prevent and control dengue.

Sustainable Cold Chain Management: An Evaluation of Predictive Waste Management Models

The integration of advanced predictive models is pivotal for optimizing demand forecasting and inventory management in cold chain logistics. This study evaluates the application of machine learning techniques—ARIMA (Auto-Regressive Integrated Moving Average) and Multiple Linear Regression (MLR)—to forecast demand trends and analyze key drivers in a mid-sized cold chain operation. Trained on a multi-year sales dataset, the ARIMA model excelled in capturing seasonal patterns, while the MLR model effectively incorporated multivariable factors such as temperature, product type, and promotional activity. Both models demonstrated strong predictive accuracy, with low Mean Absolute Error (MAE) and Root Mean Squared Error (RMSE), offering reliable and computationally efficient solutions for mid-sized operations. The findings underscore the novelty of combining ARIMA’s time-series capabilities with MLR’s multivariable analysis to address complex demand drivers. By aligning with Resource-Based View (RBV) and Supply Chain Resilience Theory, this research advances the understanding of AI-driven predictive models as strategic tools for enhancing operational efficiency, reducing waste, and promoting sustainability in cold chain logistics. This work sets the stage for future innovations in AI-driven supply chain optimization.

INDIA AT 2050: FORECASTING INDIA'S GDP USING AUTOREGRESSIVE INTEGRATED MOVING AVERAGE (ARIMA)

The global power structure has evolved dramatically since World War II, transitioning from a bipolar world through unipolar dominance to today's multipolar reality. While the United States maintains significant influence, emerging powers like China and Russia, alongside an increasingly assertive Global South, are reshaping international dynamics. This transformation has given rise to ‘Collaborative Coexistence,' where nations prioritize pragmatic cooperation over ideological alignment. Within this context, India's emergence, particularly since 2014, represents a remarkable story of economic growth and diplomatic maturity. The country now stands as an economic competitor to the US and China while pursuing an independent political path, balancing neutrality with active participation in addressing global challenges. Drawing strength from its democratic foundations and multilateral approach, India has gained substantial international influence. Economic projections using ARIMA (Auto Regressive Integrated Moving Average) methodology suggest India's economy could exceed USD 27 trillion by 2050. This paper employs ARIMA (2,1,3) and examines this trajectory through 2050, arguing that these developments position India to define what may become the 'Indian Century.'

Modelling and Forecasting Future Retail Price of Capsicum Annum L. Var. Kulai for Food Security and SDG Issues in Perlis, Malaysia

Objective: This study focuses on the modeling and forecasting of the retail price of Capsicum Annum L. Var. Kulai in Perlis, Malaysia, as a measure to support food security initiatives. Theoretical Framework: Food security is a pressing global issue exacerbated by factors such as climate change, conflicts, and the COVID-19 pandemic. Malaysia, ranked 41st in The Global Food Security Index (GFSI) 2022, has seen a concerning rise in food insecurity, driven by increased agricultural input costs and a high dependency on food imports. Method: Using historical monthly time series data from January 2018 to May 2023, various univariate time series models were employed, including Naïve, Seasonal Naïve, Holt’s Method, and ARIMA models. Results and Discussion: The study found that Holt’s Method provided the most accurate forecasts, with a mean absolute percentage error (MAPE) of 0.4607. The model predicts a continued increase in chili prices, which could pose challenges to food security in the region. Research Implications: These findings underscore the importance of accurate price forecasting in formulating effective agricultural policies and supporting local communities in mitigating food insecurity. This research contributes to worldwide initiatives aimed at fulfilling SDGs for goal 2 (Zero Hunger and Sustainable Agriculture), goal 11 (Sustainable Cities and Communities), and goal 13 (Climate Action). Originality/Value: This study offers valuable insights into forecasting the price of Capsicum Annum L. Var. Kulai in Perlis, Malaysia. Food security challenges have increasingly affected this area as various univariate time series models have been applied, and Holt’s method has been identified as the most effective. Providing policymakers with reliable forecasts guide strategic agricultural policies and supports food security efforts.

Assessing Water Temperature and Dissolved Oxygen and Their Potential Effects on Aquatic Ecosystem Using a SARIMA Model

Temperature and dissolved oxygen (DO) are of critical importance for sustainable aquatic ecosystem and biodiversity in the river systems. This study aims to develop a data-driven model for forecasting water quality in the Athabasca River using a seasonal autoregressive integrated moving average model (SARIMA) for forecasting monthly DO and water temperature. DO and water temperature observed at Fort McMurray and Athabasca from 1960 to 2023 were used to train and test the model. The results show the satisfied model performance of DO with a coefficient of determination (R2) value of 0.76 and an RMSE value of 0.79 for training and 0.67 and 0.92 for testing, respectively, at the Fort McMurray station. At the Town of Athabasca station, the RMSE and R2 of DO were 0.92 and 0.72 for training and 0.77 and 0.86 for testing, respectively. For the modeled temperature, RMSE and R2 were 2.7 and 0.87 for training and 2.2 and 0.95 for testing, respectively, at Fort McMurray and were 2.0 and 0.93 for training and 1.8 and 0.97 for testing, respectively, in the Town of Athabasca. The results show that DO concentration is inversely proportional to the temperature. This implies that the DO could be related to water temperature, which, in turn, is correlated with air temperature. Therefore, the SARIMA model performed reasonably well in representing the dynamics of water temperature and DO in the cold climate river. Such a model can be used in practice to reduce the risk of low DO events.

COMPARISON OF SARIMA AND SARIMAX METHODS FOR FORECASTING HARVESTED DRY GRAIN PRICES IN INDONESIA

Harvested dry grain (HDG) is a vital commodity for rice availability and plays a strategic role in Indonesia’s agricultural economy. Farmers typically sell HDG to rice millers post-harvest, yet disparities between farm-level selling prices and consumer-level purchase prices. This price gap can lead to financial losses for farmers, highlighting the need for accurate forecasting can lead to potential losses for farmers. SARIMA models are effective in capturing seasonality and trends but often fail to incorporate external factors influencing the dependent variable, resulting in less accurate forecasts when such factors have significant impacts. SARIMAX models, however, can include exogenous variables like the government purchase price (GPP), which supports farmer income by establishing a price floor for HDG and directly influencing farm-level price dynamics. This study aims to compare the SARIMA and SARIMAX models in forecasting HDG prices at the farm level in Indonesia, using GPP as an exogenous variable. The dataset, obtained from Statistics Indonesia, covers January 2008 to March 2024, and the forecasting accuracy is measured using Mean Absolute Percentage Error (MAPE). The findings indicate that the best model is the SARIMAX model (1,1,1)(0,1,2)12, achieving a MAPE of 10.919%. The forecasted results show that HDG prices in 2024 are expected to remain stable, with only a gradual increase throughout the year.

THE COMPARISON OF ARIMA AND RNN FOR FORECASTING GOLD FUTURES CLOSING PRICES

In the financial markets, accurately forecasting the closing prices of gold futures is crucial for investors and analysts. Traditional methods like ARIMA (Autoregressive Integrated Moving Average) have been widely used for this purpose, particularly for their effectiveness in short-term stable data forecasting. However, the inherent complexity and dynamic nature of financial data, coupled with trends and seasonal patterns, present significant challenges for long-term forecasting with ARIMA. Conversely, advanced methods such as Recurrent Neural Networks (RNN) have shown promise in handling these complexities and providing reliable long-term forecasts. This research seeks to evaluate and compare the performance of ARIMA and RNN in forecasting daily gold futures closing prices using forecast accuracy tests namely RMSE and MAPE, aiming to identify the optimal method that balances accuracy, stability, and adaptability to trends and seasonal variations in the financial market. The daily data for this analysis is sourced from Investing.com (https://www.investing.com).

MODEL SELECTION FOR B-SPLINE REGRESSION USING AKAIKE INFORMATION CRITERION (AIC) METHOD FOR IDR-USD EXCHANGE RATE PREDICTION

Exchange rate data is a collection of information about the exchange rate the foreign currency which collected by time. Autoregressive Integrated Moving Average (ARIMA) is a well-known time series analysis. Several assumptions that need to be checked before running the ARIMA model are stationarity, normality, and white noise. B-spline regression is a method of modeling time series data without considering assumptions. This research aims to create a forecasting model for Rupiah exchange rate against US Dollar using B-spline regression. The B-spline regression model was generated with a combination of degrees two to four and a maximum of four knots. After that, the optimal model is selected using the Akaike Information Criterion (AIC) score. The performance of the selected model is validated using Mean Absolute Percentage Error (MAPE) values. The optimal degree is 3 (quadratic) and the optimal number of knot points is two-knot points with an AIC value of 857.8322 and a MAPE value of 0.0148376. The best model is:

Drought prediction of Henan province in China

Henan province is a key agricultural region in China, influenced strongly by sudden drought. There are relatively few methods to help farmers to make drought projections for the future. The paper tried to use previous monthly SPEI data of time series from 12 stations in Henan from 1978 to 2018 to achieve this purpose. The paper applied Seasonal ARIMA (Autoregressive Integrated Moving Average) to capture patterns of time series and forecast future 5-years value from 2019 to 2024. The terms of models including autoregressive (p), integrated (d), moving average (q) were found based on different tests in order to construct models by removing trends and seasonality of datasets. The final results are ARIMA models of 12 stations in Henan as well as future 5-years predictions of each station. Models effectively capture the main trends and patterns of time-series data; however, some complex patterns and hidden laws still exist in datasets, influencing the accuracy of forecasting. The paper proves Seasonal ARIMA and studying information from past data of SPEI can be useful for preparing drought in Henan. However, the progress in improving the accuracy of forecasting needs to be continued in the future.

IMPLEMENTATION OF CROSS-VALIDATION ON HANG SENG INDEX FORECASTING USING HOLT’S EXPONENTIAL SMOOTHING AND AUTO-ARIMA METHOD

This study applies a rolling window cross-validation to evaluate the multi-step forecasts instead of using the traditional single split for Hang Sheng Index (HSI) forecasting. The forecasting methods discussed in this study are Holt's Exponential Smoothing and auto ARIMA, chosen because of their ability to model trend data as in the daily HSI. This research aims to evaluate up to five step forecast values obtained by the two forecasting methods built in the training data with rolling window cross-validation. In the experiment, each of the 21 auto ARIMA and Holt's models was constructed from 84 observations (as in-sample data) obtained from the rolling window cross-validation. The one to five step forecast values of daily HSI are then calculated using those models, and the accuracy of each forecast value is evaluated based on Mean Absolute Percentage Error (MAPE). The results show that the Auto ARIMA model produces a lower MAPE value than Holt's model, namely 2.9196%, 4.6553%, 6.4012%, 8.3083%, and 10.3781%, respectively, for one to five steps ahead. Therefore, auto ARIMA is more recommended for forecasting HSI values up to five steps ahead than Holt's method.

Assessing the tourism efficiency in the Caspian Sea region

ABSTRACT This research studies the operational effectiveness of the tourism industry in the Caspian regions of Kazakhstan, Russia and Azerbaijan during the 2003–2022 period, with a particular emphasis on the impact of the recent crises (COVID-19, Ukrainian war). To this end, the paper uses the data envelopment analysis meta-frontier model, the Simar and Wilson regression and the autoregressive integrated moving average (ARIMA) forecasting technique. The findings indicate significant disparities in tourism regional performance, with Kazakhstan and Azerbaijan particularly affected by the pandemic and the Ukrainian War. Forecasts indicate potential growth in the tourism industry of the Republic of Kalmykia, Russia, contingent on specific conditions.

Post-Recession Recovery in US Air Transport: Forecasting with a Temporal Causal Model

This study examines the causal relationship between air transport demand and socio-economic indicators, with a focus on post-recession recovery dynamics. Using monthly data from 1990 to 2022, the research explores causality between air transport indicators and socio-economic indicators, based on which a temporal causal model for forecasting is created. A temporal causal model, integrating air transport and socio-economic metrics, is introduced to improve passenger air transport forecasting. Forecasted values from the temporal causal model and an ARIMA model were compared with actual realized traffic to assess the quality and accuracy of the models. Based on the comparison, the temporal causal model enables instant analysis of circumstances and causes in dynamic environments, as well as reliable forecasting of upcoming intermediate periods. This research contributes to airlines and other air transport stakeholders by delivering a reliable short-term forecasting tool for informed decision-making and sustainable growth.