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Time series forecasting using dynamic particle swarm optimizer trained neural networks
Time series forecasting is a very important research area because of its practical
application in many elds. Due to the importance of time series forecasting, much
research e ort has gone into the development of forecasting models and in improving
prediction accuracies. The interest in using arti cial neural networks (NNs) to model
and forecast time series has been growing. The most popular type of NN is arguably the
feedforward NN (FNN). FNNs have structures capable of learning static input-output
mappings, suitable for prediction of non-linear stationary time series. To model nonstationary
time series, recurrent NNs (RNNs) are often used. The recurrent/delayed
connections in RNNs give the network dynamic properties to e ectively handle temporal
sequences. These recurent/delayed connections, however, increase the number of weights
that are required to be optimized during training of the NN.
Particle swarm optimization (PSO) is an e cient population based search algorithm
based on the social dynamics of group interactions in bird
ocks. Several studies have
applied PSO to train NNs for time series forecasting, and the results indicated good
performance on stationary time series, and poor performance on non-stationary and
highly noisy time series. These studies have assumed static environments, making the
original PSO, which was designed for static environments, unsuitable for training NNs
for forecasting many real-world time series generated by non-stationary processes.
In dealing with non-stationary data, modi ed versions of PSOs for optimization in
dynamic environments are used. These dynamic PSOs are yet to be applied to train
NNs on forecasting problems. The rst part of this thesis formulates training of a FNN
forecaster as a dynamic optimization problem, to investigate the application of a dynamic
PSO algorithm to train FNNs in forecasting time series in non-stationary environments.
For this purpose, a set of experiments were conducted on ten forecasting problems under
nine di erent dynamic scenarios. Results obtained are compared to the results of FNNs
trained using a standard PSO and resilient backpropagation (RPROP). The results show
that the dynamic PSO algorithm outperform the PSO and RPROP algorithms. These
ndings highlight the potential of using dynamic PSO in training FNNs for real-world
forecasting applications.
The second part of the thesis tests the hypothesis that recurrent/delayed connections
are not necessary if a dynamic PSO is used as the training algorithm. For this purpose,
set of experiments were carried out on the same problems and under the same dynamic
scenarios. Each experiment involves training a FNN using a dynamic PSO algorithm,
and comparing the result to that obtained from four di erent types of RNNs (i.e. Elman
NN, Jordan NN, Multi-Recurrent NN and Time Delay NN), each trained separately
using RPROP, standard PSO and the dynamic PSO algorithm. The results show that
the FNNs trained with the dynamic PSO signi cantly outperform all the RNNs trained
using any of the algorithms considered. These ndings show that recurrent/delayed
connections are not necessary in NNs used for time series forecasting (for the time series
considered in this study) as long as a dynamic PSO algorithm is used as the training
method.