Generalized autoregressive moving average models

• 成果类型: Article
• 署名作者: Benjamin, MA; Rigby, RA; Stasinopoulos, DM
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1198/016214503388619238
• 发表日期: 2003
• 页码: 214-223
• 关键词: maximum-likelihood-estimation; time-series; regression-models; linear-models

摘要

A class of generalized autoregressive moving average (GARMA) models is developed that extends the univariate Gaussian ARMA time series model to a flexible observation-driven model for non-Gaussian time series data. The dependent variable is assumed to have a conditional exponential family distribution given the past history of the process. The model estimation is carried out using an iteratively reweighted least squares algorithm. Properties of the model, including stationarity and marginal moments, are either derived explicitly or investigated using Monte Carlo simulation. The relationship of the GARMA model to other models is shown, including the autoregressive models of Zeger and Qaqish, the moving average models of Li, and the reparameterized generalized autoregressive conditional heteroscedastic GARCH model (providing the formula for its fourth marginal moment not previously derived). The model is demonstrated by the application of the GARMA model with a negative binomial conditional distribution to a well-known time series dataset of poliomyelitis counts.