Special Issue 2022 – Call for Papers
A New Role for Statistics: The Joint Special Issue of "Statistics in Transition New Series" (SiTns) and "Statystyka Ukraïny" (SU)
Sanusi Alhaji Jibrin https://orcid.org/0000-0003-1276-7965 , Rosmanjawati Abdul Rahman https://orcid.org/0000-0002-5384-0674

© Sanusi Alhaji Jibrin, Rosmanjawati Abdul Rahman. Article available under the CC BY-SA 4.0 licence


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This article defines the Autoregressive Fractional Unit Root Integrated Moving Average (ARFURIMA) model for modelling ILM time series with fractional difference value in the interval of 1 < d < 2. The performance of the ARFURIMA model is examined through a Monte Carlo simulation. Also, some applications were presented using the energy series, bitcoin exchange rates and some financial data to compare the performance of the ARFURIMA and the Semiparametric Fractional Autoregressive Moving Average (SEMIFARMA) models. Findings showed that the ARFURIMA outperformed the SEMIFARMA model. The study’s conclusion provides another perspective in analysing large time series data for modelling and forecasting, and the findings suggest that the ARFURIMA model should be applied if the studied data show a type of ILM process with a degree of fractional difference in the interval of 1 < d < 2.


interminable long memory, autocorrelation, fractional unit root integrated series, fractional unit root differencing, ARFURIMA model


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