IntroductionThe price of crude oil as an essential commodity in the world economy shows a pattern and identifies the component factors that influence it in the short and long term. The long pattern of the price movement of crude oil is identified by a fractionally time series model where the accuracy can still be improved by making a hybrid residual model using a fuzzy time series approach.MethodsTime 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 are indicated by a high level of fluctuation and the autocorrelation value between lags that decreases slowly. However, a more accurate model is proposed as a hybridization time series model with fuzzy time series Markov chain (FTSMC).ResultsThe time series data collected from the monthly period of West Texas Intermediate (WTI) oil price as the standard for world oil prices for the 2003–2021 time period. The data of WTI oil price has a long-memory data pattern to be modeled fractionally, and subsequently their hybrids. The times series model of crude oil price is obtained as the new target model of hybrid ARIMA and ARFIMA with FTSMC, denoted as ARIMA-FTSMC and ARFIMA-FTSMC, respectively.DiscussionThe 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.
Asuransi jiwa merupakan suatu produk yang berguna untuk mengurangi risiko yang datang secara tiba-tiba di masa mendatang. Asuransi jiwa dwiguna adalah salah satu jenis asuransi jiwa yang memberikan dua manfaat sekaligus yaitu memberikan uang pertanggungan ketika tertanggung meninggal dunia atau memberikan uang pertanggungan ketika tertanggung masih hidup hingga akhir masa pertanggungan. Tertanggung memiliki kewajiban untuk membayarkan premi yang disimpan perusahaan asuransi sebagai cadangan untuk menutupi klaim oleh tertanggung. Premi dapat dihitung dengan tabel mortalitas dan hukum mortalitas Gompertz. Salah satu metode perhitungan cadangan yaitu yaitu Metode Full Preliminary Term. Perhitungan cadangan dengan hukum mortalitas Gompertz dan tanpa hukum mortalitas Gompertz memberikan hasil yang sama pada akhir pertanggungan sesuai dengan kontrak yang disepakati. Namun, apabila terjadi klaim di pertengahan perhitungan cadangan tanpa hukum mortalitas Gompertz memberikan hasil lebih baik .Diterima: Direvisi: Dipublikasikan :Kata Kunci: Cadangan, Metode Full Preliminary Term, Hukum Mortalitas Gompertz
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