## 1 Introduction
Since the creative method of combining forecasts was introduced by Bates and Granger in 1969 [28], this approach has been utilized to address practical forecasting issues across various fields. Examples include wind power generation forecasting [29], electricity load forecasting [30, 31], and parameter inversion for mining subsidence prediction [32]. Combined models allow for the comprehensive utilization of information contained within an individual model, resulting in enhanced predictive accuracy compared to the individual model [33]. Combined forecasting models can be divided into two categories: one is the fixed-weight combined model, where the weights assigned to individual predictive models remain constant throughout the forecasting process; the other is the variable-weight combined model, where different weights can be assigned to individual models based on various constraint criteria. Given that individual models exhibit varying levels of accuracy in predicting subsidence at different times, using a variable-weight combination approach is more reasonable. The key focus of combination forecasting lies in determining the weights. Currently, most combined models use the criterion of minimizing the sum of squared prediction errors to determine these weights [34]. In addition to this method, there are other approaches such as the entropy weighting method [35, 36] and improved coefficient of variation weight ing [37]. In this paper, based on these three fixed-weight methods, we introduced a sliding window model [38] to transition from fixed to variable weights. This addressed the shortcomings of individual time function models and fixed-weight combined models and aimed to enhance the predictive accuracy of the combined model. This model, based on a fixed sliding window size, continually shifted to the next window to segment the entire subsidence measurement data, allowing us to obtain more localized subsidence information while considering the overall data trends. Combining this with the fixed-weight determination method, we assigned weights to the data within each window, thereby achieving the overall goal of variable weighting. To ensure a more reasonable determination of the window size instead of relying on manual assignment as utilized in the past [39], this paper employed the entropy weighting method to calculate the sliding window size. This paper employed the concept of combination modeling and utilized a sliding window approach to transform previously fixed weights into variable weights. This approach constructed a variable-weight combined model, thereby improving the accuracy of dynamic surface subsidence prediction. Firstly, we analyzed the impact of various parameters in different models on the subsidence curve and use the trust-region reflective algorithm (TRF) [40] to determine the optimal parameters for the time function model. Secondly, by introducing the idea of combination modeling, we combined different individual time function models. Building upon the previous combined model with fixed weights, we introduced the sliding window mechanism to achieve the goal of variable weighting, resulting in the creation of variable-weight combined model. In comparison to the individual time function model, the variable-weight combined model exhibited higher predictive accuracy, providing a new approach and method to further enhance the dynamic prediction of surface subsidence via time function models.