Time-Series Modeling Based on a Modified Volterra Neural Network

This paper proposes a novel neural network model that integrates a modified Volterra digital filter with a feedforward neural network for time-series modeling. In the proposed architecture, all input signals in the conventional Volterra filter are replaced by corresponding output signals, since time-series problems typically consist of observable output sequences over time without explicit external inputs. These output signals, together with their cross-product terms, are constructed as input vectors for the feedforward neural network. To optimize the network parameters, including weights and thresholds, the well-known particle swarm optimization (PSO) algorithm is employed. Based on the proposed PSO-trained neural network model, two types of time series are investigated: chaotic time series and financial time series involving exchange rates. For each case, multiple independent runs with different initial conditions are conducted to ensure the robustness of the proposed method. Furthermore, the effects of varying filter orders and population sizes on modeling performance are also examined.