Non-Gaussian ARMA Models

摘要: We discuss stationary AR and ARMA time series models for sequences of integer-valued random variables continuous variables. Stationary distribution these is non-Gaussian. Such can be broadly described as extensions Gaussian models, which have been very widely discussed in the literature. These non-Gaussian share two important properties with a linear AR(1) model: (i) conditional expectation \(X_t\) function past observation (ii) auto-correlation (ACF) has an exponential decay. However, variance frequently observations. are formed so to specific form distribution. distributions include standard discrete such binomial, geometric, Poisson, exponential, Weibull, gamma, inverse Gaussian, Cauchy. In some cases, maximum likelihood estimation tractable. other regularity conditions not met. Estimation then carried out based on marginal process mixing strong or \(\phi \)-mixing useful derive estimators.