Modelling time series with temporal and spatial correlations in transport planning using hierarchical ARIMA-copula Model: A Bayesian approach

Time series analysis has been used extensively in transport research in areas such as traffic operations, transport planning, safety and environmental sustainability. The frequentist time series modelling is a dominant approach to estimate model parameters, typically by maximising the likelihood function, the least-squares method or the generalised method of moments. In contrast, the Bayesian approach determines a posterior distribution for the model parameters based on the data and the parameters' prior distributions. Bayesian analysis might be challenging as requires high computational estimations. However, efficient algorithms, such as Markov chain Monte Carlo (MCMC), and the emergence of powerful computing facilities have made this type of analysis more attractive. While Bayesian approaches have gained increasing attention, transport research on time series data has been chiefly inclined toward frequentist-based models. This study provides insights into the inference and prediction of hierarchical Bayesian ARIMA models developed for time series transport data. Using the Metropolis-Hastings algorithm for the posterior inference, we illustrate the statistical properties of our approach. In addition, a Bayesian copula model has been developed to present the correlation between multivariate time series data. The developed joint model provides a fully Bayesian hierarchical ARIMA-copula model that can model both temporal and spatial correlations. The Bayesian approach for approximating posterior distributions model parameters makes the Bayesian model a viable substitute to the frequentist model whenever the frequentist model parameters cannot be estimated due to complications associated with maximising the likelihood function or a small sample. We then demonstrate practical implementations of the models examined in realworld cases where the model's performance is compared with the vector auto-regression (VAR) model.