Weighted discrete ARMA models for categorical time series
提出了一类灵活的加权离散ARMA模型，用于处理名义或有序分类时间序列，能捕捉负序列依赖或相邻状态更易转移等特征，并推导了平稳性等性质，通过模拟和实际数据展示了其优势。
A new and flexible class of ARMA‐like (autoregressive moving average) models for nominal or ordinal time series is proposed, which are characterized by using so‐called weighting operators and are, thus, referred to as weighted discrete ARMA (WDARMA) models. By choosing an appropriate type of weighting operator, one can model, for example, nominal time series with negative serial dependencies, or ordinal time series where transitions to neighboring states are more likely than sudden large jumps. Essential stochastic properties of WDARMA models are derived, such as the existence of a stationary, ergodic, and ‐mixing solution as well as closed‐form formulae for marginal and bivariate probabilities. Numerical illustrations as well as simulation experiments regarding the finite‐sample performance of maximum likelihood estimation are presented. The possible benefits of using an appropriate weighting scheme within the WDARMA class are demonstrated by a real‐world data application.