It is popular to develop the city-wide Parking Guidance System (PGS) in China nowadays, in order to alleviate the parking difficulties arising in large cities. Prediction on parking occupancy is the essential intelligent technology to help vehicles find the proper parking lot efficiently in PGS. And the known prediction methods have to be powered by real-time data, without which would cause error accumulation and significant inaccuracies. In the early stage of PGS deployment, however, it is very hard to collect the real-time data from the parking lots all over the city. Therefore, this study takes the historical data of non-stationary parking spaces with periodic characteristics as the research object. Firstly, statistical analysis of parking spaces is carried out according to the central limit theorem and Law of Large Numbers. Then, we propose a method named SAL (non-stationary Stochastic And Long short-term memory) combined with LSTM (Long Short-Term Memory), to predict the parking occupancy at the given time, based on digging the history data. Experimental data prove that compared with using LSTM and Lyapunov exponent method, SAL has lower computational complexity, more accurate prediction, and effectively solves the problem of error accumulation caused by multi-step long-term prediction without real-time data.