Discrete Time Series Generated by Mixtures Ii: Asymptotic Properties

Summary The darma (discrete mixed autoregressive-moving average) processes are a broad but parametrically simple class of models for a stationary sequence of dependent discrete random variables. A darma process is formed as a random linear combination of independent identically distributed discrete random variables. The process is specified by the distribution of the independent variables, which is also the marginal distribution of the random process, and several other chosen parameters which independently determine the covariance structure of the process. In this paper the asymptotic properties of the darma process are studied. Limiting results for estimates of moments, percentiles and quantiles are obtained. Asymptotic properties of the χ2 test for goodness-of-fit for the marginal distribution of the process are also studied.