Capturing long-memory properties in road fatality rate series by an autoregressive fractionally integrated moving average model with generalized autoregressive conditional heteroscedasticity: A case study of Florida, the United States, 1975-2018

Modelling low temporal, large spatial data of fatal crashes: An application of negative binomial GSARIMAX time series

Road traffic injuries represent a critical public health concern, particularly in developing nations such as Iran, where the incidence of fatal crashes is escalating. Addressing this issue effectively requires sophisticated analytical methodologies to elucidate and mitigate the multifaceted factors contributing to traffic fatalities. This study introduces the Negative Binomial Generalized Seasonal Autoregressive Integrated Moving Average with Exogenous Variables (GSARIMAX) model as an innovative approach for analyzing low temporal (daily) and large spatial count data of fatal crashes over a ten-year period (March 2014 to March 2022) in Iran. Unlike traditional models that predominantly focus on aggregated monthly or high-resolution data, the proposed negative binomial GSARIMAX model leverages daily count data, accommodating over-dispersion inherent in crash counts and providing a more granular and accurate analysis across extensive spatial regions. The model integrates significant exogenous variables, including traffic volume, maximum and minimum temperatures, wind speed, and wind direction, alongside harmonic seasonal components to capture both annual and semi-annual periodic fluctuations in crash occurrences. Model performance was rigorously evaluated using Deviance Information Criterion (DIC) and Mean Absolute Relative Error (MARE) metrics, alongside out-of-sample predictive accuracy assessments. The negative binomial GSARIMAX (0,1,2)-SOH model demonstrated superior performance compared to the Gaussian GSARIMAX counterpart, evidenced by lower MARE and DIC values. Notably, traffic volume and maximum temperature emerged as significant predictors of fatal crashes, while seasonal harmonic terms further enhanced model accuracy by effectively capturing temporal dynamics. The Bayesian estimation framework employed facilitates robust inference and the analysis of posterior predictive distributions, affirming the Negative Binomial GSARIMAX model's superior fit and forecasting capabilities. These findings underscore the model's potential advantages over conventional Gaussian statistical methods, particularly in handling low temporal resolution and large spatial datasets. Moreover, dynamic models incorporating exogenous variables demonstrated enhanced predictive performance, highlighting the importance of integrating diverse factors in crash analysis. This study not only advances the methodological landscape for traffic crash analysis but also provides actionable insights for policymakers and safety authorities. By identifying key determinants of fatal crashes and accounting for seasonal variations, the Negative Binomial GSARIMAX model serves as a valuable tool for informing targeted interventions aimed at reducing traffic fatalities. Future research should extend this approach by incorporating additional environmental and behavioral variables and conducting comparative analyses across multiple provinces to capture a broader spectrum of influencing conditions.

Influence of road safety policies on the long-term trends in fatal Crashes: A Gaussian Copula-based time series count model with an autoregressive moving average process

Time series analysis plays a vital role in modeling historical crash trends and predicting the possible changes in future crash trends. In existing safety literature, earlier studies employed multiple approaches to model long-term crash risk profiles, such as integer-valued autoregressive Poisson regression model, integer-valued generalized autoregressive conditional heteroscedastic model, and generalized linear autoregressive and moving average models. However, these modeling frameworks often fail to fully capture several key properties of crash count data, especially negative serial correlation, and nonlinear dependence structures across temporal crash counts. To address these methodological gaps in existing safety literature, this study proposes to use a Gaussian Copula-based model for the long-term crash trend analysis. Specifically, this study proposes to use a Gaussian Copula-based Time Series Count Model with an Autoregressive Moving Average Process for the analysis of long-term trends in fatal crashes. The proposed approach can accommodate several data properties, which include (1) non-negative discrete property of count data, (2) positive and negative serial correlations among time series data, and (3) nonlinear dependence among time-series observations. The performance of the Gaussian Copula-based time series count model is compared with the generalized linear autoregressive and moving average model. The proposed modeling approaches are demonstrated by using yearly fatal crash count data for the years 1986 through 2022 from Queensland, Australia. The major safety interventions implemented in Queensland over those years are also highlighted to assess the possible and plausible impacts of these safety interventions in reducing fatal crash risks. Further, elasticity effects and overall percentage changes in fatal crashes across different time points are computed to demonstrate the implications of the proposed model. The policy analysis exercise shows that the implemented road safety interventions are likely to have diminishing marginal returns, underscoring the need for new and effective road safety policies to achieve the goal of zero fatalities within the set timeframe.

Time series analysis-based seasonal autoregressive fractionally integrated moving average to estimate hepatitis B and C epidemics in China

BACKGROUND

Hepatitis B (HB) and hepatitis C (HC) place the largest burden in China, and a goal of eliminating them as a major public health threat by 2030 has been set. Making more informed and accurate forecasts of their spread is essential for developing effective strategies, heightening the requirement for early warning to deal with such a major public health threat.

AIM

To monitor HB and HC epidemics by the design of a paradigmatic seasonal autoregressive fractionally integrated moving average (SARFIMA) for projections into 2030, and to compare the effectiveness with the seasonal autoregressive integrated moving average (SARIMA).

METHODS

Monthly HB and HC incidence cases in China were obtained from January 2004 to June 2023. Descriptive analysis and the Hodrick-Prescott method were employed to identify trends and seasonality. Two periods (from January 2004 to June 2022 and from January 2004 to December 2015, respectively) were used as the training sets to develop both models, while the remaining periods served as the test sets to evaluate the forecasting accuracy.

RESULTS

There were incidents of 23400874 HB cases and 3590867 HC cases from January 2004 to June 2023. Overall, HB remained steady [average annual percentage change (AAPC) = 0.44, 95% confidence interval (95%CI): -0.94-1.84] while HC was increasing (AAPC = 8.91, 95%CI: 6.98-10.88), and both had a peak in March and a trough in February. In the 12-step-ahead HB forecast, the mean absolute deviation (15211.94), root mean square error (18762.94), mean absolute percentage error (0.17), mean error rate (0.15), and root mean square percentage error (0.25) under the best SARFIMA (3, 0, 0) (0, 0.449, 2)12 were smaller than those under the best SARIMA (3, 0, 0) (0, 1, 2)12 (16867.71, 20775.12, 0.19, 0.17, and 0.27, respectively). Similar results were also observed for the 90-step-ahead HB, 12-step-ahead HC, and 90-step-ahead HC forecasts. The predicted HB incidents totaled 9865400 (95%CI: 7508093-12222709) cases and HC totaled 1659485 (95%CI: 856681-2462290) cases during 2023-2030.

CONCLUSION

Under current interventions, China faces enormous challenges to eliminate HB and HC epidemics by 2030, and effective strategies must be reinforced. The integration of SARFIMA into public health for the management of HB and HC epidemics can potentially result in more informed and efficient interventions, surpassing the capabilities of SARIMA.

SARIMA Modelling Approach for Forecasting of Traffic Accidents

To achieve greater sustainability of the traffic system, the trend of traffic accidents in road traffic was analysed. Injuries from traffic accidents are among the leading factors in the suffering of people around the world. Injuries from road traffic accidents are predicted to be the third leading factor contributing to human deaths. Road traffic accidents have decreased in most countries during the last decade because of the Decade of Action for Road Safety 2011–2020. The main reasons behind the reduction of traffic accidents are improvements in the construction of vehicles and roads, the training and education of drivers, and advances in medical technology and medical care. The primary objective of this paper is to investigate the pattern in the time series of traffic accidents in the city of Belgrade. Time series have been analysed using exploratory data analysis to describe and understand the data, the method of regression and the Box–Jenkins seasonal autoregressive integrated moving average model (SARIMA). The study found that the time series has a pronounced seasonal character. The model presented in the paper has a mean absolute percentage error (MAPE) of 5.22% and can be seen as an indicator that the prognosis is acceptably accurate. The forecasting, in the context of number of a traffic accidents, may be a strategy to achieve different goals such as traffic safety campaigns, traffic safety strategies and action plans to achieve the objectives defined in traffic safety strategies.