Hinton's deep auto-encoder (DAE) with multiple restricted Boltzmann machines (RBMs) is trained by the unsupervised learning of RBMs and fine-tuned by the supervised learning with error-backpropagation (BP). Kuremoto et al. proposed a deep belief network (DBN) with RBMs as a time series predictor, and used the same training methods as DAE. Recently, Hirata et al. proposed to fine-tune the DBN with a reinforcement learning (RL) algorithm named "Stochastic Gradient Ascent (SGA)" proposed by Kimura & Kobayashi and showed the priority to the conventional training method by a benchmark time series data CATS. In this paper, DBN with SGA is invested its effectiveness for real time series data. Experiments using atmospheric CO2 concentration, sunspot number, and Darwin sea level pressures were reported.