An Estimation Method of Neural Networks for Nonlinear Time Series Using Correration Algorithm

Recently, the extended correlation least mean squares(ECLMS) algorithm have been proposed to solve the double-talk problem in the echo canceling system. The characteristic of ECLMS algorithm is to utilize the correlation functions of the input signal instead of the input signal itself. ECLMS algorithm, based on the linear filter can separete noise signal from observed signal. This algorithm can not be used for nonlinear time series. To solve this problem, we have proposed the ECLMS algorithm for second-order Volterra filters. However, The number of operations required to consider all combination increases exponentially with the highest order term of the Volterra filter.

So, we propose Neural networks(NN) system for nonlinear time series estimation using ECLMS algorithm. It is easy to extend for the highest order term of the Volterra filter. Some numerical examples are presented to illustrate that the proposed method can work well for estimating nonlinear time series with ARCH errors.