{"title":"ARFURIMA models: simulations of their properties and application","authors":"S. A. Jibrin, Rosmanjawati Binti Abdul Rahman","doi":"10.2478/stattrans-2022-0017","DOIUrl":null,"url":null,"abstract":"Abstract 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.","PeriodicalId":37985,"journal":{"name":"Statistics in Transition","volume":"23 1","pages":"69 - 87"},"PeriodicalIF":0.0000,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Statistics in Transition","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.2478/stattrans-2022-0017","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"Mathematics","Score":null,"Total":0}
引用次数: 0
Abstract
Abstract 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.
本文定义了自回归分数阶单位根积分移动平均(ARFURIMA)模型，用于对区间为1 < d < 2的分数阶差分值的ILM时间序列进行建模。通过蒙特卡罗仿真验证了ARFURIMA模型的性能。此外，使用能源序列、比特币汇率和一些金融数据提出了一些应用，以比较ARFURIMA和半参数分数阶自回归移动平均(SEMIFARMA)模型的性能。结果表明，ARFURIMA优于SEMIFARMA模型。本研究的结论为分析大型时间序列数据进行建模和预测提供了另一种视角，研究结果表明，如果研究数据显示的ILM过程在1 < d < 2的区间内存在一定程度的分数差异，则应应用ARFURIMA模型。
期刊介绍：
Statistics in Transition (SiT) is an international journal published jointly by the Polish Statistical Association (PTS) and the Central Statistical Office of Poland (CSO/GUS), which sponsors this publication. Launched in 1993, it was issued twice a year until 2006; since then it appears - under a slightly changed title, Statistics in Transition new series - three times a year; and after 2013 as a regular quarterly journal." The journal provides a forum for exchange of ideas and experience amongst members of international community of statisticians, data producers and users, including researchers, teachers, policy makers and the general public. Its initially dominating focus on statistical issues pertinent to transition from centrally planned to a market-oriented economy has gradually been extended to embracing statistical problems related to development and modernization of the system of public (official) statistics, in general.
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