The Golden ratio has played an important role in musical composition, architecture, visual art, science, and increasingly in signal processing [1,2,3]. Underlying many of these applications are several extensions of the golden proportions including the Golden p-Section by Stakhov, the generalized Golden section by Bradley, and others [4,5]. In this paper we review and introduce generalizations of the Golden ratio. We show that there exists a fundamental connection between the limit of two consecutive terms of recursive sequences, the generalized (p, q)-Golden ratio and the Golden ratio generated by the characteristic equation. We apply these generalizations to forecasting financial time series to illustrate one of their applications in signal processing.