ARIMAX Model Research Articles

Prediction of atmospheric temperature in Sacramento area based on ARIMA and ETS models

Abstract. As global temperatures increased by 1.1 Celsius degrees, there has unprecedented shifts in climate systems. With the rising impact of global warming, exploring the warming trend helps to better understand and maintain the local environment and economy. This study focuses on predicting atmospheric temperature in the Sacramento area using ARIMA and ETS models. The research uses the temperature data from Sacramento Airport's Automated Surface Observing System (ASOS) and explores the prediction performance of ARIMA, ETS, and ARIMAX models in predicting daily average temperatures. The results indicate the ARIMAX (1,1,1) model is the most suitable for forecasting this temperature data with the lowest AIC and RMSE values. However, there are still challenges, in particular the dependence of the ARIMAX model on future exogenous variables, which leads to the forecast outcomes less accurate. To enable this ARIMAX models have better prediction performance, incorporating more exogenous variables is a potential solution. Therefore, the methods discussed in this paper provides ideas for the atmospheric temperature forecasting and points out the direction for further research.

Assessment of the COVID-19 impact on the Brazilian Unified Health System (SUS) financing: an analysis of the financing dynamics of 2020 and 2021

BackgroundAfter the establishment of the public health emergency of international concern in 2020, health systems worldwide and in Brazil observed the need to apply more extraordinary logistical efforts and possibly resources to combat the imminent pandemic.MethodsUsing the historical series of public expenditures of the National Health Fund (FNS), 2015 to 2021, the number of confirmed cases of COVID-19, and a seasonal ARIMAX model, we sought to assess how the increase in the new virus infections affected the systematic financing of the SUS in Brazil.ResultsThere were signs of seasonality and an increasing trend in the expenditure variable, which in practical terms, only indicated that the resource contributions followed an increasing trajectory already underway before the advent of the pandemic. The 1% increase in COVID-19 cases, with a one-month lag, contributes to the 0.062% increase in the variation in FNS expenditures but a decrease of 0.058% with a two-month lag.ConclusionThe tests showed no evidence to confirm a positive shift on FNS spending growth trajectory due to the increase of COVID-19 cases, only observing a significant increase one month after the occurrence of COVID cases, probably due to their worsening after this period, which was followed by a similar and comparable decrease in percentage of growth in the following month.

Exploring the influence of environmental indicators and forecasting influenza incidence using ARIMAX models.

Influenza is a respiratory infection that poses a significant health burden worldwide. Environmental indicators, such as air pollutants and meteorological factors, play a role in the onset and propagation of influenza. Accurate predictions of influenza incidence and understanding the factors influencing it are crucial for public health interventions. Our study aims to investigate the impact of various environmental indicators on influenza incidence and apply the ARIMAX model to integrate these exogenous variables to enhance the accuracy of influenza incidence predictions. Descriptive statistics and time series analysis were employed to illustrate changes in influenza incidence, air pollutants, and meteorological indicators. Cross correlation function (CCF) was used to evaluate the correlation between environmental indicators and the influenza incidence. We used ARIMA and ARIMAX models to perform predictive analysis of influenza incidence. From January 2014 to September 2023, a total of 21,573 cases of influenza were reported in Fuzhou, with a noticeable year-by-year increase in incidence. The peak of influenza typically occurred around January each year. The results of CCF analysis showed that all 10 environmental indicators had a significant impact on the incidence of influenza. The ARIMAX(0, 0, 1) (1, 0, 0)12 with PM10(lag5) model exhibited the best prediction performance, as indicated by the lowest AIC, AICc, and BIC values, which were 529.740, 530.360, and 542.910, respectively. The model achieved a fitting RMSE of 2.999 and a predicting RMSE of 12.033. This study provides insights into the impact of environmental indicators on influenza incidence in Fuzhou. The ARIMAX(0, 0, 1) (1, 0, 0)12 with PM10(lag5) model could provide a scientific basis for formulating influenza control policies and public health interventions. Timely prediction of influenza incidence is essential for effective epidemic control strategies and minimizing disease transmission risks.

Impact of climatic factors on water quality parameters in tilapia broodfish ponds and predictive modeling of pond water temperature with ARIMAX

Climate change represents a considerable threat to aquatic ecosystems, potentially affecting various water quality parameters.The study aims to assess the impacts climatic factors on the water quality parameters in tilapia broodfish pond and forecasting of water temperature in a tilapia broodfish pond using the ARIMAX model. Daily longitudinal time series data on water quality parameters were collected from the pond, while monthly climatic data were obtained from the Bangladesh Meteorological Department. Water temperature exhibited seasonal variation, peaking at 31.23 °C in October and dropping to 20.8 °C in December. pH levels ranged from 7.36 to 10.32, with the lowest recorded in December and the highest in August. Dissolved oxygen levels varied from 7.09 mg/L to 10.65 mg/L, with the lowest in September and the highest in January. Ammonia levels were highest in February at 0.33 mg/L. Water transparency ranged from 15.37 to 28 inches, with the highest in January and the lowest in June. Climatic factors significantly influenced these variations, as specified by Canonical correlation analysis (CCA). The best-fitting model, ARIMAX (1, 0, 1), indicated a fluctuating trend influenced by important exogenous factors like air temperature and solar intensity. By the end January 2025, the water temperature is expected to rise to 27.93 °C. This is a noticeable increase started from November to January. These higher temperatures may improve tilapia broodfish growth and development earlier. But the temperatures are predicted to drop started from February to March, which could negatively affect tilapia growth and development. A clear seasonal fluctuating pattern is exhibited in the future. These findings provide important insights for researchers, policymakers, academics, and those involved in tilapia farming. By considering air temperature and solar intensity in planning, stakeholders can better anticipate future pond conditions. Developing adaptive management strategies to reduce negative impacts and make the most of favorable conditions will be essential for sustainable tilapia production in the context of climate change.

ARIMAX-Threshold 모형을 이용한 20대 이하 마약류 사범 검거 수 시계열 분석

In recent years, the number of drug offenders under 20s has surged, accounting for approximately 35.5% of all drug offenders in 2023, which becomes a serious social issue in Korea. The purpose of this work is to study and compare time series models for statistical analysis and prediction for the number of drug offenders under 20s. ARIMA and ARIMAX model is applied to the data of the number of drug offenders arrested under 20s. In order to further improve the predictability, a model added by threshold, reflecting the presence or absence of the exogenous variable, is proposed and compared. As for the exogenous variable, dark web data that is directly related to the number of drug offenders arrested, as a main drug dealer, is used. Based on cross-correlation coefficient analysis, the ARIMAX-Threshold model including indicator variables and threshold is proposed. Out-of-sample forecasting analysis is performed to compare the forecasting performance, and it is revealed that the ARIMAX-Threshold model proposed in this study improves the forecasting errors by up to 9.4%. The predicted values and prediction intervals of the data on the number of drug offenders under 20s until April 2025 are presented, which will contribute to help in policy development for drug crime prevention.

Assessing the variability in chlorophyll-a and covariates in Arabian Sea using ARIMAX model and wavelet coherence approaches

The Arabian Sea is one of the most productive regions in the global ocean. In the present study, relationship of Chl-a with environmental parameters have been studied in the Arabian Sea. The Autoregressive Integrated Moving Average with explanatory variable (ARIMAX) models namely ARIMAX (1,0,1), ARIMAX (2,0,3), ARIMAX (5,0,4), ARIMAX (7,0,6), ARIMAX (8,0,8), ARIMAX (11,0,9) and ARIMAX (12,0,11) were tested. After evaluation, ARIMAX (2,0,3) and ARIMAX (12,0,11) were identified as the best fit models and can be used to model Chl-a in the Arabian Sea. Wavelet coherence approach was applied to understand the relationship of Chl-a with rainfall, sensible heat flux, remote sensing at 443 nm, aerosol optical depth, black carbon deposition and calcite concentration. Two strips of high correlation in the frequency bands of 4–8 and 8–16 significant at 95% level were observed in each wavelet coherence diagram except for remote sensing reflectance at 443 nm and sensible heat flux.

Development of an ARIMAX model for forecasting airport electricity consumption in Accra-Ghana: The role of weather and air passenger traffic

The rapid expansion of the aviation industry has significantly increased energy consumption within airport terminals. This study introduces an advanced ARIMAX model to forecast electricity consumption at Kotoka International Airport (KIA) in Ghana by incorporating weather conditions and air passenger numbers. By analysing data from 2019 to 2022, including lockdown periods, the model demonstrates superior predictive accuracy, evidenced by an RMSE of 55,914 kWh, a MAPE of 4.22 %, and an R-squared value of 0.899. Key determinants of energy consumption identified include air passengers and temperature, highlighting their substantial impact on energy use. The ARIMAX model's accuracy underscores its potential for enhancing energy management practices at airports. By integrating variables such as air passenger traffic and weather conditions, the model refines energy demand predictions, supporting more efficient energy use and operational planning. The ARIMAX model proves to be a valuable tool for forecasting energy consumption at KIA, aiding in energy management and sustainability efforts.

Impact of Weather on Incidence and Mortality of COVID-19: An Application of the ARIMAX Model

Impact of Weather on Incidence and Mortality of COVID-19: An Application of the ARIMAX Model

ARIMAX Modelling: Response of Hass Avocado Respiration Rate to Environmental Factors

This research explores how random events influence the respiration rate in Hass avocado beyond deterministic models in order to develop better strategies for extending its shelf life. Understanding these factors can enhance the accuracy of postharvest management strategies. The Autoregressive Integrated Moving Average (ARIMA) model with exogenous variables (ARIMAX) is an alternative stochastic probability model which is capable of modeling complex, externally influenced phenomena such as respiration. This study aimed to elucidate the effect of three exogenous variables, namely temperature, relative humidity, and ambient illumination, on the respiration rate of Hass avocado fruits. Data on the respiration rate and exogenous variables were obtained using sensors coupled to a data acquisition system in a prototype of continuous airflow. The Box–Jenkins methodology was employed to construct the ARIMA models. The temperature, relative humidity, ambient illumination, and respiration rate variables were adjusted to the ARIMA models (3,1,2), ARIMA (1,1,2), ARIMA (1,1,2), and ARIMA (1,1,3), respectively. The ARIMAX (1,1,3) models were obtained from the pre-whitened respiration rate series. The impact detected in the transfer functions indicates increases in the respiration rate of 0.34%, 1.52%, and 0.99% for each unit increase in the temperature, relative humidity, and ambient illumination variables, respectively. In this regard, ARIMAX modeling is reliable for explaining the physiological response of Hass avocado fruits due to external factors. In future research, it is intended to extrapolate this stochastic modeling procedure to measure the effect of dynamic loads on the respiratory metabolism of fruits during transportation, where there is a considerable loss in the quality of fresh products.

PERAMALAN JUMLAH PENUMPANG BUS RAPID TRANSIT (BRT) BANJARBAKULA DENGAN METODE AUTOREGRESSIVE INTEGRATED MOVING AVERAGE WITH EXOGENOUS VARIABLE (ARIMAX) DENGAN EFEK VARIASI KALENDER

Banjarbakula Bus Rapid Transit (BRT) is an inner-city bus-based mass transit system that provides a sense of comfort, safety, speed in mobility, and low cost in serving the citizens of Banjarmasin City and Banjarbaru City. Based on data on the number of passengers on the Banjarbakula BRT for the period April 2020 - February 2023, public interest in using the Banjarbakula BRT as a mode of transportation is quite high. However, the limited units and operational schedules make the Banjarbakula BRT unable to fully meet the needs of the public. Forecasting the number of passengers of BRT Banjarbakula for the next 12 periods is one of the measures to prepare the infrastructure, quality and units of BRT Banjarbakula in order to facilitate the public and create a better transportation system. In the Banjarbakula BRT passenger data, there is an increase in the number of passengers at certain times such as during religious holidays and school holidays, so this increase in passenger numbers is thought to be due to the influence of the calendar variation effect. This research intends to forecast the number of passengers of BRT Banjarbakula using the best ARIMAX model with the effect of calendar variation. The results indicate that the ARIMAX (0, 1, 1) model is the best ARIMAX model to forecast the number of passengers of BRT Banjarbakula for the next 12 periods. The forecast results indicate an increase in the month where the Christmas celebration and also the memorial haul guru sekumpul, so that the variable Christmas celebration and memorial haul guru sekumpul significantly affect the number of passengers of BRT Banjarbakula.Keywords: Forecasting, BRT Banjarbakula, ARIMAX with calendar variation effects

Daily Rainfall Forecasting with ARIMA Exogenous Variables and Support Vector Regression

There is a seasonal element every year, with the dry season often lasting from May to October and the rainy season lasting from November to April. However, climate change causes the changing of the rainy and dry seasons to be erratic, so it is necessary to anticipate weather conditions. Prediction of rainfall is used to see natural conditions in the future with time series modeling. The rainfall modeling method at the six Surabaya observation posts used is the Autoregressive Integrated Moving Average with exogenous variables (ARIMAX) and Support Vector Regression. The exogenous variable used is the captured seasonal pattern of rainfall. The SVR model uses input lags from the ARIMAX model and parameter tuning uses the Kernel Radial Based Function. Selection of the best model uses the minimum RMSE value. The results showed that the average occurrence of rain at the six rainfall observation posts occurred in January, February, March, April, November and December. The ARIMAX method in this study is well used to predict rainfall in Gubeng and rainfall in Wonorejo. The SVR input lag ARIMAX method is good for predicting rainfall for Keputih, Kedung Cowek, Wonokromo and Gunung Sari. Nonparametric methods are better used to forecast rainfall data because they are able to capture data patterns with greater volatility than parametric methods, one of which is the SVR method.

Research on the relationship between global oil prices and economic indicators based on linear regression and ARIMAX models

This report aims to analyze the relationship between global oil prices and various economic indexes by using linear regression and ARIMAX models. This study will predict global oil prices accurately and establish a reasonable system for regulating oil prices. The research uses the statistical approach to predict oil prices based on historical data (including independent variables and dependent variable). The study uses monthly average data of WTI crude oil prices from January 2000 to March 2023 and contains the analysis of various economic indicators such as Consumer Price Index (CPI), Personal Consumption Expenditures (PCE), Employment, Population, and Oil Price. The findings indicate that the linear regression model can explain about 40.89% of the variation in log oil price, with significant negative effects of log_PCE, log_EMPLOYMENT, and log_POPULATION, and a significant positive effect of CPI on log_price. However, there exists the probability that some other factors have impact on oil prices. In this study, the author employ the ARIMAX model with ARIMA(4,1,1) errors, which can describe a relatively good fit and small errors in training set measures. Overall, while the linear regression model partially explains the variability in global oil prices, further analysis on residuals is necessary. The study concludes that the ARIMAX model provides a better approach to capture the time-series nature of the data.

Traffic crash prediction in Kano, Nigeria: multivariate long short-term memory method

Accurate traffic crash prediction is crucial for implementing effective road safety measures. In this study, the performance of long short-term memory (LSTM) and multivariate LSTM (MLSTM) models in forecasting total crash count data in Kano state, Nigeria were compared. Human and vehicle factors, including speed violations, tyre bursts, brake failures, sign/light violations and phone use while driving, were incorporated as covariates in the MLSTM model. An autoregressive integrated moving average with exogenous variables (Arimax) model was used to investigate the effects of the covariates. The MLSTM model outperformed both the basic LSTM model and individual covariate models, emphasising the synergistic effect of considering a broad range of factors. The Arimax model results revealed that speed violation is significantly positively correlated with total crashes; the other covariates showed positive correlations but did not reach the statistical significance. The findings underscore the importance of a multivariate approach in enhancing traffic crash prediction. The MLSTM model's superior performance highlights the value of considering a comprehensive range of factors that influence crash occurrence to achieve more accurate predictions. Practical applications of these models could involve leveraging them for proactive traffic safety measures, including increased enforcement of traffic rules, improvements to road infrastructure and targeted driver education and campaigns.

Impact of Standardised Packaging of Tobacco Products Regulations on cigarette consumption and youth smoking in England: interrupted time-series analysis

BackgroundIn the UK in May 2016, standardised packaging of tobacco products was implemented, including minimum pack sizes of 20 sticks or 30 g loose tobacco. The change was intended to...

Comprehensive forecasting of California’s energy consumption: A multi-source and sectoral analysis using ARIMA and ARIMAX models

California’s significant role as the second-largest consumer of energy in the United States underscores the importance of accurate energy consumption predictions. With a thriving industrial sector, a burgeoning population, and ambitious environmental goals, the state’s energy landscape is dynamic and complex. This paper presents a comprehensive analysis of California’s energy consumption trends and provides detailed forecasting models for different energy sources and sectors. The study leverages ARIMA and ARIMAX models, considering both historical consumption data and exogenous variables. We address the unique challenges posed by the COVID-19 pandemic and the limited data for 2022, highlighting the resilience of these models in the face of uncertainty. Our analysis reveals that while fossil fuels continue to dominate California’s energy landscape, renewable energy sources, particularly solar and biomass, are experiencing substantial growth. Hydroelectric power, while sensitive to precipitation, remains a significant contributor to renewable energy consumption. Furthermore, we anticipate ongoing efforts to reduce fossil fuel consumption. The forecasts for energy consumption by sector suggest some decline in the commercial and residential sectors, reflecting California’s recently declining population and the shift away from brick-and-mortar shops and offices to online websites and remote work. In contrast, the industrial and transportation sectors are expected to experience some growth until they return to more constant pre-COVID levels.

A Coupled Statistical and Deterministic Model for Forecasting Climate-Driven Dengue Incidence in Selangor, Malaysia.

The mosquito-borne dengue virus remains a major public health concern in Malaysia. Despite various control efforts and measures introduced by the Malaysian Government to combat dengue, the increasing trend of dengue cases persists and shows no sign of decreasing. Currently, early detection and vector control are the main methods employed to curb dengue outbreaks. In this study, a coupled model consisting of the statistical ARIMAX model and the deterministic SI-SIR model was developed and validated using the weekly reported dengue data from year 2014 to 2019 for Selangor, Malaysia. Previous studies have shown that climate variables, especially temperature, humidity, and precipitation, were able to influence dengue incidence and transmission dynamics through their effect on the vector. In this coupled model, climate is linked to dengue disease through mosquito biting rate, allowing real-time forecast of dengue cases using climate variables, namely temperature, rainfall and humidity. For the period chosen for model validation, the coupled model can forecast 1-2weeks in advance with an average error of less than 6%, three weeks in advance with an average error of 7.06% and four weeks in advance with an average error of 8.01%. Further model simulation analysis suggests that the coupled model generally provides better forecast than the stand-alone ARIMAX model, especially at the onset of the outbreak. Moreover, the coupled model is more robust in the sense that it can be further adapted for investigating the effectiveness of various dengue mitigation measures subject to the changing climate.

Comparison of the Symmetric and Asymmetric Generalized Autoregressive Conditional Heteroscedasticity (GARCH) Models in Forecasting the 2018-2023 Jakarta Composite Index

The Autoregressive Integrated Moving Average with Exogenous Variables (ARIMAX) method assumes a homogeneous residual variance, but data with high volatility can cause violations of this assumption. Hence, it is interesting to compare the forecasting accuracy of symmetric and asymmetric Autoregressive Conditional Heteroskedasticity (ARCH) models in various data conditions. The research aimed to compare the accuracy of the symmetric ARCH/ Generalized Autoregressive Conditional Heteroscedasticity (GARCH) and asymmetric TGARCH models in forecasting weekly Jakarta Composite Index (JCI) data on January 1st, 2018, to April 24th, 2023, by involving the influence of COVID-19 as a covariate variable and applying several validation scenario models to training and testing data. Based on the best-selected model, forecasting was carried out from May 1st, 2023, to July 3rd, 2023. The data used were weekly JCI opening data from January 1st, 2018, to April 24th, 2023, with the COVID-19 period as a covariate variable. The analysis results show that symmetric and asymmetric methods can handle violations of the heteroscedasticity assumption in the ARIMAX model. The best model produced based on four data validation scenarios is the asymmetric ARIMAX(3,1,3)-TGARCH(1,2) model with an average MAPE value of 3.158%. In this model, the COVID-19 variable significantly influences the JCI movement. Forecasting is done with forecasting results that are stable with confidence intervals that widen in each period.

Enhanced S‐ARIMAX model performance and state‐of‐health prediction accuracy with battery pack degradation factor combinations

AbstractThis study addresses the critical need for accurate state‐of‐health (SOH) predictions in lithium‐ion batteries, crucial for maintaining efficient battery operation and extending lifespan. We propose a novel approach utilizing the Seasonal autoregressive integrated moving average with exogenous variables (S‐ARIMAX) model, integrating multiple battery degradation factors as exogenous variables for precise SOH estimation. Our methodology involves correlation analysis to identify optimal factors, which are then incorporated into distinct cases of the S‐ARIMAX model. We evaluate the model's performance using mean absolute percentage error (MAPE) and identify voltage deviation as a highly correlated exogenous variable significantly impacting predictive accuracy. Notably, our findings underscore the S‐ARIMAX model's superiority in longer cycles, demonstrating a MAPE as low as 0.1113 at 160 cycles, emphasizing the model's adeptness at capturing cyclic patterns for precise long‐term SOH forecasts. Comparing S‐ARIMAX and ARIMAX models highlights the pivotal role of seasonality, particularly in long‐term predictions. The study's quantitative findings emphasize the necessity of integrating highly correlated variables and accounting for seasonal patterns in optimizing lithium‐ion battery SOH predictions. Our approach presents practical implications for maintaining battery performance and lifespan in electric vehicles and energy storage systems, underlining the importance of selecting strongly correlated variables and integrating seasonal components for accurate and reliable SOH forecasts.

Comparative analysis of different approaches to the Ukrainian residential property market evolution modelling and its forecast for the years 2019–2024

PurposeThis study aims to provide a comprehensive analysis of various approaches to the residential property market evolution modelling and to examine the macroeconomic fundamentals that have shaped this market development in Ukraine in recent years.Design/methodology/approachThe study uses a comprehensive data set encompassing relevant macroeconomic indicators and historical apartment prices. Multifactor linear regression (MLR) and ridge regression (RR) models are constructed to identify the impact of multiple predictors on apartment prices. Additionally, the ARIMAX model integrates time series analysis and external factors to enhance modelling and forecasting accuracy.FindingsThe investigation reveals that MLR and RR yield accurate predictions by considering a range of influential variables. The hybrid ARIMAX model further enhances predictive performance by fusing external indicators with time series analysis. These findings underscore the effectiveness of a multidimensional approach in capturing the complexity of housing price dynamics.Originality/valueThis research contributes to the real estate modelling and forecasting literature by providing an analysis of multiple linear regression, RR and ARIMAX models within the specific context of property price prediction in the turbulent Ukrainian real estate market. This comprehensive analysis not only offers insights into the performance of these methodologies but also explores their adaptability and robustness in a market characterized by evolving dynamics, including the significant influence of external geopolitical factors.

Forecasting The Price Of Shallots And Red Chilies Using The ARIMAX Model

Shallots and red chilies are superior vegetable crops and contribute quite a lot to the development of the national economy. Prices of these two commodities fluctuate almost every year. At certain times the price of both commodities soared due to high demand while supply in the market was insufficient. So, it is necessary to do an analysis to see what phenomena have a significant influence on the increase in the price of shallots and red chilies. The method used in this study is ARIMAX with exogenous variables, namely variables dummy monthly and various religious holiday calendars such as Chinese New Year, Eid al-Fitr, and Eid al-Adha. The results of the analysis show that the price of shallots is influenced by calendar variations one month after Chinese New Year and one month before Idul Fitri. Meanwhile, the price of red chilies is influenced by the month before Chinese New Year, during Chinese New Year, and a month after Chinese New Year, a month before Eid al-Fitr and during Eid al-Fitr, a month before Eid al-Adha and during Eid al-Adha. Shallots and red chilies ARIMAX models obtained a MAPE value of 17.36% and 25.62%.