Neural Networks Approach - Computational Intelligence in Time Series Forecasting - page 132

Figure 3.19(b). The combination of forecasts using a 2-6-6-1 artificial neural network

In our practical example, the first 150 input-output samples were used to train
the network. Thereafter, the values of the interconnecting weights and biases are
saved for network performance testing using the remaining 151 to 224 samples of
data. From the experimental results shown in Figure 3.19(a) and Figure 3.19(b) and
Table 3.1, it is obvious that the network output very closely matches the actual
time series, indicating that a nonlinear combination of the forecasts is better than
the individual forecasts.

3.6.4 Forecasting of Multivariate Time Series

Chakraborty et al. (1992) conducted experimental investigations on forecasting of
multivariate time series using neural networks. They focused their attention on the
statement that, in the case of substantial cross-correlation of individual variables of
multivariable time series data, the forecasting accuracy of each variable can be
improved when simultaneously changing the values of other variables within the
time series is taken into account. This has been observed in multivariate statistical
analysis when, based on observation data, identifying the interdependencies of
variables involved in a multivariate system. To prove this, Chakraborty et al.
(1992) analyzed the one-step and multistep prediction behaviour of a trivariate
time series

in the interval of t = 1-100 samplings using

x [, xx x , ]

t 123 t t t

x separate modelling of each component of the multivariable time series,
interpreted as mutually independent univariate time series
x combined modelling , by simultaneous consideration of all three variables
x statistical modelling , using the statistical model developed by Tiao and
Tsay (1989).