Particle swarm optimization performance for fitting of Lévy noise data

The feasibility of particle swarm optimization in fitting the Lévy noise data is examined. Lévy noise is a kind of non-Gaussian noise widely used in fractional and fractal calculus and in many other engineering applications. All type of functions, ranging from linear to polynomial and exponential, are studied after adding different levels of Lévy noise. The mean squared error is used to evaluate the particle swarm optimization performances. These performances are compared to the accuracy of the least square error. This work proves that particle swarm optimization is much more accurate than least square error, which is widely used in parameter identification for Gaussian and less appropriately used for non-Gaussian noise data. Particle swarm optimization is much more accurate than the least squares method, especially for nonlinear functions.