AUTHOR=Devianto Dodi , Ramadani Kiki , Maiyastri  , Asdi Yudiantri , Yollanda Mutia 

TITLE=The hybrid model of autoregressive integrated moving average and fuzzy time series Markov chain on long-memory data

JOURNAL=Frontiers in Applied Mathematics and Statistics

VOLUME=Volume 8 - 2022

YEAR=2022

URL=https://www.frontiersin.org/journals/applied-mathematics-and-statistics/articles/10.3389/fams.2022.1045241

DOI=10.3389/fams.2022.1045241

ISSN=2297-4687

ABSTRACT=Time series data containing long memory elements can be modified into a stationary model through the Autoregressive Fractional Integrated Moving Average (ARFIMA). This fractional model can provide better accuracy on long memory data than the classic Autoregressive Integrated Moving Average (ARIMA) model. The long memory data is indicated by a high level of fluctuation and the autocorrelation value between lags that decreases slowly. However, a more accurate model for long-memory data is needed. The proposed new target model is a hybrid of ARIMA and ARFIMA with Fuzzy Time Series Markov Chain (FTSMC), denoted as ARIMA-FTSMC and ARFIMA-FTSMC, respectively. The time-series data used is the monthly period of West Texas Intermediate (WTI) oil price, the standard for world oil prices for the 2003-2021 time period. WTI oil price has a long memory data pattern to be modeled fractionally, and subsequently their hybrids.  The accuracy model measured by MAE, RMSE, and MAPE shows that the hybrid model of ARIMA-FTSMC has better performance than ARIMA and ARFIMA, but the hybrid model of ARFIMA-FTSMC provides the best accuracy compared to all models. The superiority of the hybrid time series model of ARFIMA-FTSMC  on long memory data provides an opportunity for the hybrid model as the best and more precise forecasting method.