Skylight background subtraction is an important part of LAMOST 1D spectral data processing, and constructing ideal super sky spectral models is of great significance since it may directly affect the quality of the spectral products. Generally, the super sky spectral models are composed of the spectra from sky fibres simultaneously observed with target objects, and sky background may be of regular variation along with different observation times. Taking full account of these timing features, the super skylight model can be effectively corrected to improve the skylight reduction effect. Meanwhile, the trajectory clustering method is an effective tool for analyzing the characteristics of the target with temporal and spatial variation. Therefore, a method for analyzing the characteristics of the sky spectra based on the trajectory clustering is provided in this paper orienting to the possible variation laws in the sky spectra of LAMOST. It includes the following 3 parts: (1) the time series description of sky spectra. In fact, LAMOST pipeline uses and provides the instant super sky spectra for each observed target. In order to obtain the light-changing characteristics of the sky background spectra of a specific sky area, the time series of sky spectra are re-described by selecting the sky fiber spectra and background spectra without target component, taking the 5-degree field of view (the Fov of LAMOST) as processing unit, and evenly grouping these spectra by observation date. (2) density-based clustering algorithm (STK-means) for sky spectra. In order to solve the problem that the random parameters may lead to relatively poor convergence and clustering, a density-based similarity measurement formula is studied. The values of this formula are used as the selection basis of the initial parameters, and then a new algorithm named STK-means is proposed after updating the traditional k-means algorithm. (3) experiment analysis. Firstly, by experiment, the correctness and effectiveness of this method is verified, and clustering effect is analyzed by utilizing different initial parameter k. And then, the trajectory characteristics of sky spectral time series are analyzed by selecting the sky spectra from one of complete small sky areas in the first phase of LAMOST survey. The experimental results show that the sky background in particular region is distributed symmetrically around the lunar 15th and 16th of each month, which indicates the influence partly from the moon phase during the observation process in this sky area. These timing characteristics can be quantified to correct the super sky spectral model. Meanwhile, uniform sampling of data during the description of time-series spectra is very important, so this method can be effectively applied to the regions of high celestial number density such as GAC, disk, halo, etc. On the contrary, the longer time survey is necessary for the low number density areas. In addition, this method may also effectively find outlier sky spectra of specific regions, which will provide rare samples for further physical study.