Efficient Multistep Nonlinear Time Series Prediction involving Deterministic Chaos based Local Reconstruction methodologies and Multilayer Perceptron Neural Networks in Diode Resonator Circuits

Abstract: - A novel non-linear signal prediction method is presented using non linear signal analysis and deterministic
chaos techniques in combination with an improved local reconstruction methodology and multilayer
neural networks for a diode resonator chaotic circuit generated time series forecasting. Multisim is used
to simulate the circuit and show the presence of chaos as well as to generate the time series data. The Time series
analysis is performed by the method proposed by Grasberger and Procaccia, involving estimation of the
correlation and minimum embedding dimension as well as of the corresponding Kolmogorov entropy. These
parameters are used to construct the preprocessing step of a first stage of a one step / multistep predictor. This
first stage involves, in the sequel a local reconstruction based approach. More specifically, it is suggested that
by extracting a class of informative features coming from second order information, involving the topology of
their neighbouring state vectors, from the state vectors of the local reconstruction approach then, significantly
better results could be obtained with respect to chaotic time series reconstruction. In the second stage of the
proposed method a multilayer neural network, trained with the conjugate gradient algorithm, is employed in
order to provide the proper topology preserving error characteristics for the associated time series prediction.
One of the novelties of the proposed two stage predictor lies on that the ANN involved could be employed as
second order predictors, that is as error predictors of the non-linear signal analysis based forecasted values.
This novel two stage chaotic signal forecasting technique is evaluated through an extensive experimental
study.
Keywords:- time series forecasting, non-linear signal analysis, diode, chaos, time series, correlation dimension,
prediction, error prediction, neural networks, local reconstruction, Backpropagation error