Determination of the fuzzy relation stage in the fuzzy time series
methods is very important for forecast performance. Aladag et al.
(2012) proposed a first order fuzzy time series method. In this
paper, this method is successfully improved for a high order fuzzy
time series forecasting model. According to the application results,
the proposed method has better forecasting performance than
many other methods in the literature. Because the proposed method
is based on the high order fuzzy time series forecasting model, real
life time series can bewell forecasted. Moreover, the proposedmethod
takes into consideration all membership vales. It should not be
forgotten that the performance of the proposed method can change
for different data sets. It is not easy to say it will outperform other
methods for every data set. As a result of implementation, it can be
seen that the proposed method can produce good forecasts for the
three stock exchange data sets. Although the proposedmethod is improved
to a high order form, the order selection is an important
problem for it. In future studies, order selection for the proposed
method can be achieved by using optimization techniques. If some
new techniques applied in the fuzzification and defuzzification
stages, a better forecasting performance could be obtained from the
proposed method. In the future, proposed method can be easily
modified for better forecasting performance and multivariate fuzzy time series models. Although fuzzy time series methods can produce
good forecasts, the confidence intervals for forecasts cannot be obtained.
It can be said that this is a very big challenge for nonprobabilistic
forecasting methods. Obtaining confidence intervals of
forecasts for the proposed method will be considered in future
studies.