Stationarity of generalized autoregressive moving average models

Stationarity of Generalized Autoregressive Moving Average Models

Time series models are often constructed by combining nonstationary effects such as trends with stochastic processes that are believed to be stationary. Although stationarity of the underlying process is typically crucial to ensure desirable properties or even validity of statistical estimators, there are numerous time series models for which this stationarity is not yet proven. A major barrier...

Some Autoregressive Moving Average Processes with Generalized Poisson Marginal Distributions

Abstrac t . Some simple models are introduced which may be used for modelling or generating sequences of dependent discrete random variables with generalized Poisson marginal distribution. Our approach for building these models is similar to that of the Poisson ARMA processes considered by Al-Osh and Alzaid (1987, J. Time Ser. Anal., 8, 261-275; 1988, Statist. Hefte, 29, 281-300) and McKenzie (...

Modified Maximum Likelihood Estimation in First-Order Autoregressive Moving Average Models with some Non-Normal Residuals

When modeling time series data using autoregressive-moving average processes, it is a common practice to presume that the residuals are normally distributed. However, sometimes we encounter non-normal residuals and asymmetry of data marginal distribution. Despite widespread use of pure autoregressive processes for modeling non-normal time series, the autoregressive-moving average models have le...

Dierential Geometry of Autoregressive Fractionally Integrated Moving Average Models

The di erential geometry of autoregressive fractionally integrated moving average processes is developed. Properties of Toeplitz forms associated with the spectral density functions of these long memory processes are used to compute the geometric quantities. The role of these geometric quantities on the asymptotic bias of the maximum likelihood estimates of the model parameters and on the Bartl...

Maximum Likelihood Identification of Gaussian Autoregressive Moving Average Models