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STS425 Arifah B. et al.
standard (short-memory) stochastic volatility models cannot be used to
forecast the CPO Price. Breidt et al. (1998) suggested a long memory stochastic
volatility (LMSV) model in discrete time to overcome the limitations of the
previous models. In LMSV model, the log-volatility is simulated as an
autoregressive fractional integrated moving average (ARFIMA) process. The
well-defined of LMSV in the mean square sense is one of main advantages
that facilitates the establishing the stochastic features of LMSV model.
Moreover, the LSMV model has counterparts in models for level series. These
models gives their statistical properties to the LSMV model.
Karia et al. (2013a) applied ARFIMA model to solve the nonstationary
persistency of the prices of CPO in the long-run data. They conducted a
comparison between the ARFIMA over the existing ARIMA model and the
results indicates that the ARFIMA model outperformed the existing ARIMA
model. Karia et al. (2013b) forecasted the CPO price in Malaysia by using both
the artificial neural network (ANN) and adaptive neuro fuzzy inference system
(ANFIS). The predictability accuracy of ANN and ANFIS approaches was
illustrated in regard with the statistical forecasting approach such as ARFIMA
model. Their findings showed that the ANN model gives better results
compared to the ANFIS and ARFIMA models. However, both models have a
complicated time series characteristics and had relatively more parameters
and consequently they need a bigger amounts of data. Karia et al. (2015)
selected five different edible oils prices that have long memory behavior to
investigate the effect of the over difference on the prices of these oils. They
conducted a comparison by using the time series data that recorded with the
over difference and long memory behavior between ARIMA and ARFIMA
models. Their findings show mixed results for that the forecasting of oil prices
for the two models and the existing of over difference seems not to have a
significant effect neither ARIMA nor ARFIMA models. They also found that
ARFIMA model does not give poor out-sample forecasting. Rahim et al. (2018)
used weighted subsethood-based algorithm to generate fuzzy rules of
predictions that are embedded in fuzzy time series data. This method is
considered as a new approach to forecast the CPO price in order to enhance
the accuracy of future prediction. They compared their model with previous
models and with numerical results and the outcomes shows an increase in
accuracies from the proposed method in predicting CPO price.
In Fact, volatility estimation is considered as a one of the complicated
process in econometrics since the volatility can not be observed directly. There
are no ideal method neither to simulate volatility nor to collect volatility data.
To select the method we should consider many aspects such as financial
support, data, expertise and manpower. Chen et al. (2017) evaluated the
degree of persistence property of the data by constructing LMSV model. The
model is developed by using fractional Ornstein-Uhlenbeck (fOU) process in

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