Neuro-fuzzy Approach - Computational Intelligence in Time Series Forecasting - page 248

previous example for forecasting purposes the time series data X = { X 1 , X 2 , X 3 ,…,
X q } were rearranged in a multi-input single-output (XIO)-like structure. For
modelling and forecasting of the given time series the respective neuro-fuzzy
predictor that has to be developed is taken to have four inputs ( n = 4) and one
output ( m = 1). In addition, both the sampling interval and the lead time of forecast
is supposed to be six time units, so that for each t > 18 the input data represents a
four-dimensional vector
XI( t -18) = [ X ( t -18), X ( t -12), X ( t -6), X ( t )],
and the output data a scalar value
XO( t -18) = [ X ( t +6)].
In the forecasting example considered, using Equation (6.44) and neglecting the
first 100 transient data from the chaotic series, in addition 1000 input-output data
were generated for the XIO matrix. Out of 1000 generated input-output data, only
the first 200 data sets were used for network training, and the remaining 800 data
were used for verification of forecasting results.
The training and forecasting performances achieved with the implemented
neuro-fuzzy network and with stored seven fuzzy rules are illustrated in Figure
6.8(a) and Figure 6.8(b) and listed in Table 6.2(a) and also compared with other
standard models in Table 6.2(b). The items listed in serial numbers 1 to 12 of Table
6.2(b) were taken from Kim and Kim (1997), whereas serial number 13 is taken
from Park et al. (1999). The results clearly confirm excellent training and
forecasting performance of the Takagi-Sugeno-type neuro-fuzzy network for
Mackey-Glass chaotic time series.