Exploring Long-Memory Process in the Prediction of Interval-Valued Financial Time Series and Its Application

Long-memory process has been widely studied in classical financial time series analysis, which has merely been reported in the field of interval-valued financial time series. The aim of this paper is to explore long-memory process in the prediction of interval-valued time series (IvTS). To model the long-memory process, two novel interval-valued time series prediction models named as interval-valued vector autoregressive fractionally integrated moving average (IV-VARFIMA) and ARFIMAX-FIGARCH were established. In the developed long-memory pattern, both of the short term and long-term influences contained in IvTS can be included. As an application of the proposed models, interval-valued form of WTI crude oil futures price series is predicted. Compared to current IvTS prediction models, IV-VARFIMA and ARFIMAX-FIGARCH can provide better in-sample and out-of-sample forecasts.