Analysis of Time Series with Artificial Neural Networks

This paper presents the study of time series in gravitational lensing to solve the time delay problem in astrophysics. The time series are irregularly sampled and noisy. There are several methods to estimate the time delay between this kind of time series, and this paper proposes a new method based on artificial neural networks, in particular, General Regression Neural Networks (GRNN), which is based on Radial Basis Function (RBF) networks. We also compare other typical artificial neural network architectures, where the learning time of GRNN is better. We analyze artificial data used in the literature to compare the performance of the new method against state-of-the-art methods. Some statistics are presented to study the significance of results.