Copula ARMA-GARCH modelling of spatially and temporally correlated time series data for transportation planning use

Abstract

Time series analysis has been used extensively in transport research in various areas, such as traffic management and transport planning. Time-series data may contain temporal and spatial correlations. Temporal correlation refers to the dependency of observations on time, while spatial correlation refers to the dependence of observations on space. Although there is a substantial amount of literature on statistical models that modelled temporal correlation of transport time-series data, there are few studies that accommodate both temporal and spatial correlations. In cases where more than one time-series dataset is collected from different locations, each observation can depend on its previous values and observations from other locations. Transport-related time-series data (e.g., traffic volumes, travel times, etc.) may exhibit nonlinear spatial correlation within the transport network. However, existing statistical time series models that consider spatial correlation, such as vector auto-regression (VAR) models, are limited to linear spatial correlation functions with a time-invariance assumption. This study introduces a copula time series model capable of modelling correlations between variables through time and space. Temporal correlations are modelled by an autoregressive moving average-generalised autoregressive conditional heteroskedasticity (ARMA-GARCH) model, where the conditional mean is predicted based on past values and errors, and conditional variance is predicted based on past residuals and conditional variances. This enables the model to describe heteroscedastic data. The spatial correlation is modelled with a copula model, which has the flexibility to model different types of correlations, such as nonlinear, tailed and asymmetric correlations. We illustrate the statistical properties of our approach where the performance of the copula ARMA-GARCH model is compared with the VAR model based on mean absolute percentage error (MAPE) and root mean square error (RMSE) values of model predictions on synthesised data. We then demonstrate practical implementations of these models examined in two case studies with traffic count data collected from four main arterial roads in Sydney.