ARFIMA and ARTFIMA Processes in Time Series with Applications

The objective of this study is to discuss different fractional time series processes, such as Autoregressive Fractional Integrated Moving Average (ARFIMA), which are also called long-memory or persistent models. Due to the very nature of long memories, these processes have an obvious bearing on forecast and are worthy of study. Another variant of these processes is Autoregressive Temporal Fractional Integrated Moving (ARTFIMA), which applies a tempered fractional difference to the standard Autoregressive Moving Average (ARMA) process. Various estimation and forecast methods are discussed, and utility of these models is illustrated with application to real data sets.