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

Abstract

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.

A Study of Nigeria Monthly Stock Price Index Using ARTFIMA-FIGARCH Hybrid Model

“…The outcomes show the superior suitability and performance of the hybrid model, specifically ARTFIMA-FIGARCH, in comparison with the mean models (ARTFIMA and ARFIMA) and the hybrid model, ARFIMA-FIGARCH, for both simulated and real-world datasets. This study is in conformity with the works of Jibrin (2019) and Kabala (2020), who are of the opinion that hybrid models outperform mean models. These findings clearly show the dominance of the ARTFIMA-FIGARCH model as a hybrid mean-volatility model over its counterpart, the ARFIMA-FIGARCH model, and are therefore considered the most suitable for studying the mean and volatility of the Nigerian Monthly Stock Price Index and other financial data that exhibit similar characteristics.…”

“…Noteworthy examples of long-memory mean models found in the literature are the Autoregressive Fractional Integrated Moving Average (ARFIMA) model proposed by Granger, Joyeux, and Hosking and the Autoregressive Tempered Fractional Integrated Moving Average (ARTFIMA) model introduced by Meershart et al, (2014). Other models in this category include the Semiparametric Fractional Autoregressive (SEMIFAR) model by Beran (1999), the Beta-ARFIMA (  -ARFIMA) model by Pumi et al (2019), and the ARFURIMA model by Jibrin (2019).…”

“…Based on the findings of this study, it is concluded that ARTFIMA-FIGARCH is considered to be the most suitable model for studying the mean and volatility of the Nigerian monthly stock price index. Almeida et al, (2017), Sivakumar and Mohandas (2009), Korkmaz et al, (2009), , Jibrin (2019), andKabala (2020).…”

New R package arfurimaaparch for Estimation of ARFURIMA-APARCH Model and Big Data Analytics

“…𝛾 is the leverage coefficient in the interval of −1 < 𝛾 < 1 and 𝛿 is the parameter for the power term that takes finite positive values. For detail derivation of the ARFURIMA and hybrid ARFURIMA-APARCH models see Jibrin (2019) and Jibrin et al, (2022).…”

Developing Exp-FIGARCH Hybrid Models for Time Series Modelling

“…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.…”