Memory properties and fractional integration in transportation time-series

In transportation analyses, autoregressive integrated moving average (ARIMA) and generalized autoregressive conditional heteroskedasticity (GARCH) models have been widely used mainly because of their well established theoretical foundation and ease of application. However, they lack the ability to capture long memory properties and do not jointly treat the mean and variance (variability) of a time-series. We employ fractionally integrated dual memory models and compare results to classical time-series models in a traffic engineering context. Results indicate that dual memory models offer better representation of the original time-series than classical models; further, forcing the differentiation parameter of ARIMA model to equal 1 leads to over-inflated moving average terms and, consequently, to questionable models with artificial correlation structures.