A recurrence-weighted prediction algorithm for musical analysis

Forecasting the future behaviour of a system using past data is an important topic. In this article we apply nonlinear time series analysis in the context of music, and present new algorithms for extending a sample of music, while maintaining characteristics similar to the original piece. By using ideas from ergodic theory, we adapt the classical prediction method of Lorenz analogues so as to take into account recurrence times, and demonstrate with examples, how the new algorithm can produce predictions with a high degree of similarity to the original sample.