A fractional difference returns for stylized fact studies

Rahman, Rosmanjawati Abdul; Alhaji, Jibrin Sanusi

doi:10.1088/1742-6596/1132/1/012074

Cited by 3 publications

(3 citation statements)

References 18 publications

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“…Many time series exhibits trend, volatility, a long memory and leverage effect (see Gajda et al, 2018;Lyócsa et al, 2019;Boubaker et al, 2020;Lembang et al, 2021;Chinhamu et al, 2022). The current study assumed that the model in (1) failed to account for the volatility, ILM, trend and leverage effect concurrently that are present and dwelled in the time series{𝑋 𝑡 }, 𝑡 = 1, … , 𝑇;have residuals{𝜀 𝒕 }, 𝑡 ≥ 0, that are serially correlated and heteroscedastic;and cannot account for the high degree of relationship that exists in absolute returns of a time series as observed for similar mean modelsby Safadi & Pereira (2010) and Rahman &Jibrin (2018).…”

Section: The Proposed Arfurima-aparch Modelmentioning

confidence: 99%

A novel hybrid ARFURIMA-APARCH model for modeling interminable long memory and asymmetric effect in time series

Jibrin¹,

Ibrahim²,

Munkaila³

2022

dujopas

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In this paper, we introduce a new hybrid model namely Autoregressive Fractional Unit Root Integrated Moving Average-Asymmetric Power Autoregressive Conditional Heteroscedasticity (ARFURIMA-APARCH) model. The Nigeria daily COVID19 records and Bitcoin to EURO exchange rate that exhibit a type of Long Memory (LM) called Interminable LM (ILM), volatility and asymmetric (leverage) effect were used to show the applications of the proposed ARFURIMA-APARCH model. The existing Autoregressive Fractional Integrated Moving Average-Asymmetric Power Autoregressive Conditional Heteroscedasticity (ARFIMA-APARCH) model were estimated and compared with the ARFURIMA-APARCH model. Results showed that the new hybrid model is better based on goodness-of-fit, serial correlation tests and forecast measures of accuracy. As a conclusion, our study showed that the ARFURIMA-APARCH model performed better compared to the ARFIMA-APARCH hybrid model. Therefore, the ARFURIMA-APARCH model is a better option for modeling ILM, volatility and leverage effect of health and financial data. Future study should focus on the application of the developed hybrid ARFURIMA-APARCH model using some major economic indicators, for example, Gross Domestic Product (GDP), currency exchange rate, stock price index, interest rate and other financial data.

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Section: The Proposed Arfurima-aparch Modelmentioning

confidence: 99%

A novel hybrid ARFURIMA-APARCH model for modeling interminable long memory and asymmetric effect in time series

Jibrin¹,

Ibrahim²,

Munkaila³

2022

dujopas

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“…There are some financial indices that are known to be nonlinear, volatile and long memory (Rahman and Jibrin (2018), Benrhmach et al (2020), Ojeda et al, (2021), de Oliveira et al, (2022), Jibrin et al, (2022), and Jiang et al, (2023)). The ExpAR-ARCH, ExpAR-GARCH and other hybrid models introduced in the time series literature lack the strength to handle these three identified time series characteristics at the same time.…”

Section: Introductionmentioning

confidence: 99%

Developing Exp-FIGARCH Hybrid Models for Time Series Modelling

Jibrin,

Osi,

Shehu

2024

dujopas

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In this paper, we introduced a new hybrid model namely Exponential Autoregressive-Fractional Integrated Generalized Autoregressive Conditional Heteroscedasticity (ExpAR-FIGARCH) model and study financial data. The Daily Nigeria All Share Stock Index that exhibit nonlinear, volatility and long memory effect were analyzed in the study. The existing ExpAR-Generalized Autoregressive Conditional Heteroscedasticity (ExpAR-GARCH) model were estimated and compared with the proposed ExpAR-FIGARCHmodel. Results showed that the new hybrid model is better based on efficient parameters, serial correlation analysis and forecast measures of accuracy. Therefore, as a conclusion, the current study indicates that the ExpAR-FIGARCHmodel performed better compared to the ExpAR-GARCHhybrid model. Therefore, the ExpAR-FIGARCHmodel is a better option for modeling nonlinear, volatility and long memory characteristics of time series. Future study should focus on the application of the developed hybrid ExpAR-FIGARCHmodel using health, meteorological and economic data.

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“…Furthermore, according to Rahman and Jibrin (2018), when the ACF of time series exhibits decays more slowly and have fractional difference value in the interval of 1 𝑑 2, the series are said to be having an Interminable LM (ILM) process. In view of this, we need a family of models that can simulate a very strong dependent relationship (autocorrelation) between distance observations, at the same time being flexible enough to model both the integrated, 𝐼 1 and Fractional Unit Root Integrated (FURI), I(1 𝑑 2) process.…”

Section: Introductionmentioning

confidence: 99%

ARFURIMA models: simulations of their properties and application

Jibrin

Rahman

2022

Statistics in Transition New Series

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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.

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A fractional difference returns for stylized fact studies

Cited by 3 publications

References 18 publications

A novel hybrid ARFURIMA-APARCH model for modeling interminable long memory and asymmetric effect in time series

A novel hybrid ARFURIMA-APARCH model for modeling interminable long memory and asymmetric effect in time series

Developing Exp-FIGARCH Hybrid Models for Time Series Modelling

ARFURIMA models: simulations of their properties and application

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