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This paper presents a Long Short Term Memory Recurrent Neural Network and Hidden Markov Model (LSTM-HMM) to predict China's Gross Domestic Product (GDP) fluctuation state within a rolling time window. We compare the predictive power of LSTM-HMM with other dynamic forecast systems within different time windows, which involves the Hidden Markov Model (HMM), Gaussian Mixture Model-Hidden Markov Model (GMM-HMM) and LSTM-HMM with an input of monthly Consumer Price Index (CPI) or quarterly CPI within 4-year, 6-year, 8-year and 10-year time window. These forecasting models employed in our empirical analysis share the basic HMM structure but differ in the generation of observable CPI fluctuation states. Our forecasting results suggest that (1) among all the models, LSTM-HMM generally performs better than the other models; (2) the model performance can be improved when model input transforms from quarterly to monthly; (3) among all the time windows, models within 10-year time window have better overall performance; (4) within 10-year time window, the LSTM-HMM, with either quarterly or monthly input, has the best accuracy and consistency. [ABSTRACT FROM AUTHOR]