Large-span spatial lattice structures generally have characteristics such as incomplete modal information, high modal density, and high degrees of freedom. To address the problem of misjudgment in the damage detection of large-span spatial structures caused by these characteristics, this paper proposed a damage identification method based on time series models. Firstly, the order of the autoregressive moving average (ARMA) model was selected based on the Akaike information criterion (AIC). Then, the long autoregressive method was used to estimate the parameters of the ARMA model and extract the residual sequence of the autocorrelation part of the model. Furthermore, principal component analysis (PCA) was introduced to reduce the dimensionality of the model while retaining the characteristic values. Finally, the Mahalanobis distance (MD) was used to construct the damage sensitive feature (DSF). The dome of Taiyuan Botanical Garden in China is one of the largest non-triangular timber lattice shells worldwide. Relying on the structural health monitoring (SHM) project of this structure, this paper verified the effectiveness of the damage identification model through numerical simulation and determined the damage degree of the dome structure through SHM measurement data. The results demonstrated that the proposed damage identification method can effectively identify the damage of large-span timber lattice structures, locate the damage position, and estimate the degree of damage. The constructed DSF had relatively strong robustness to small damage and environmental noise and has practical application value for SHM in engineering.