Evolving Takagi Sugeno (eTS) models are optimised for use in applications with high sampling rates. This mode of use produces excellent prediction results very quickly and with low memory requirements, even with large numbers of input attributes. In this paper eTS modelling is adapted for optimality in situations where memory usage and processing time are not specific requirements. The new method, eTS with memory, is demonstrated on two financial time series, both the fullband signals and after decomposition by the discrete wavelet transform. It is shown that the use of previous inputs and multiple iterations in eTS can produce better predictions for signals which are not dominated by the characteristics of noise.