**1. Introduction**

The Longmenshan fault zone is located on the eastern edge of the Qinghai-Tibet Plateau and the northwestern edge of the Sichuan Basin. It extends in a NE-SW direction, reaches the Qinling fault zone in the north, and ends at the Xianshuihe-Xiaojiang fault zone in the south. It is approximately 500 km long and 50 km wide and is mainly composed of four main faults, including the Houshan fault, Central fault, Qianshan fault, piedmont hidden fault, and the thrust nappe controlled by them [1, 2]. Dozens of important cities and towns, such as Dujiangyan, are distributed within its scope. In a southeastern direction, this large fault at the front of the main mountain

range is close to the densely populated Chengdu Plain area and the Chengdu-Chongqing economic circle. Exploring the regularity of earthquake occurrence times along the Longmenshan fault zone can provide a scientific basis for earthquake management and decision-making for earthquake prediction in this area.

Currently, earthquake research is an interdisciplinary and comprehensive field. For earthquake time series data, many researchers have used statistical and probabilistic methods to predict important information, such as earthquake occurrence time. Some scholars have focused on the exploration of magnitude time series [3–5]. There have been studies on the time interval sequence of earthquake occurrence, most of which have analyzed the probability distribution of the earthquake time interval [6–10]. There have also been studies on the prediction of time intervals. Guo & Xu [11] made a confirmatory prediction of the Ms8.0 earthquake in northwestern China using a method of multiplied periods with golden section, which appeared to be in good agreement with the testing results. Mariani and Tweneboah [12] proposed applying the stochastic differential equation based on the superposition of independent Ornstein-Uhlenbeck processes to earthquake research and used this model to fit an earthquake sequence in South America. In addition, some scholars have expanded the prediction approach, using SVM, LSTM and regression algorithms to predict earthquake times [13–16].

The seasonal autoregressive moving average model can be used not only to predict natural phenomena such as river flow and rainfall [17–20] but also to predict social and economic phenomena such as transportation passenger flow and trade volume [21–25]. In the field of earthquake prediction, some scholars have used ARIMA to identify earthquake precursor anomalies [26–29]. However, few ARIMA or SARIMA models have been used to fit earthquake occurrence time data.

In this paper, we selected earthquake events in the Longmenshan fault zone in Sichuan Province in China since 2012 as the research object. We used the SARIMA model to fit the time interval sequence according to magnitude to predict the development trend of the earthquake occurrence time interval and the time of the next earthquake occurrence.
