Abstract: Under the background of mixed frequency data with different sampling frequencies and different spacing, considering that time delay is a common phenomenon of causal action between system elements, a mixed frequency GM(1,N) modeling method with delay parameters is proposed. According to different characteristics of time delay, the models are divided into two types: GM(1,N) model with synchronous time delay and GM(1,N) model with cumulative time delay. The synchronous type is used to characterize the time-delay relationship with fixed time delay but uncertain initial time. The cumulative type is used to represent the time-delay relation of uncertain time delay length and progressive superposition of causal effect. The exponential Almon function is taken as the distribution function of time delay, which can be completely driven by data to generate various forms such as increasing, decreasing, S-type, U-type and bell type, which is helpful for mining the information of time delay in mixed frequency data. The numerical results verify the validity of the model. The model has strong applicability for the mixed frequency time-delay system with low frequency and small sample data.

Key words: mixed-frequency data, GM(1,N), time delay

摘要： 采样频率不同、间距不等的混频数据背景下,考虑时滞是系统要素间因果作用的常见现象,提出含时滞参数的混频GM(1,N)建模方法。根据时滞特征不同,将模型划分为两类:同步推移型时滞GM(1,N)模型和累积型时滞GM(1,N)模型。同步推移型用于表征时滞长度固定但起始时间不确定、具有管道延迟性质的时滞关系。累积型用于表征时滞长度不确定、因果效应逐步叠加的时滞关系。将指数Almon函数作为时滞分布函数,该函数可完全由数据驱动生成递增、递减、S型、U型、钟型等多种形态,有助于挖掘混频数据中的时滞信息。数值分析的结果验证了模型的有效性。模型对于存在低频小样本数据的混频时滞系统具有很强的适用性。

关键词: 混频数据, GM(1, N), 时滞