Considering that it is easily disturbed by various engineering factors such as weather, hydrology, and construction during engineering monitoring, the collected subsidence data contain various noises. In order to reduce the influence of engineering noise on the accuracy of subsidence prediction, it is proposed to use the Daubechies (DB) wavelet to decompose the original subsidence time series; the items with the low-frequency trend, after decomposition, are predicted using long short-term memory (LSTM) model, items with high-frequency noise used the autoregressive (AR) time series model to make predictions, and the prediction results of the low-frequency trend term and the high-frequency noise term are summed to obtain the total time series predicted value. Combining the actual engineering subsidence monitoring data of the old goaf, compared with the prediction results of the LSTM and RNN models without DB wavelet decomposition and the gray model GM (1,1), the results show that the DB wavelet has an obvious improvement effect in reducing the influence of measurement data noise on prediction error. Compared with the single prediction model LSTM, RNN, and GM (1,1), the proposed prediction model has higher prediction accuracy, smaller error, and better trend. It can be used as a calculation method to improve the prediction accuracy of surface subsidence in old goaf.