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...

The classical method of process capability analysis necessarily assumes that collected data are independent; nonetheless, some processes such as biological and chemical processes are autocorrelated and violate the independency assumption. Many processes exhibit a certain degree of correlation and can be treated by autoregressive models, among which the autoregressive model of order one (AR (1))...

Abstract We start by studying first-order autoregressive negative binomial (NBD) processes. We then compare maximum likelihood and moment based estimators of the parameters of the NBD INAR(1) model and show that the degree of dependence has significant effect on the quality of the estimators. Finally, we construct NBD processes with long-range dependence by using the NBD INAR(1) processes as ba...

Spatially Varying Autoregressive Processes Aline A. Nobre, Bruno Sansó and Alexandra M. Schmidt Scientific Computing Program, Oswaldo Cruz Foundation, Rio de Janeiro-RJ CEP:21.045-900, Brazil Department of Applied Mathematics and Statistics, University of California at Santa Cruz, Santa Cruz, CA 95064 Instituto de Matemática, Universidade Federal do Rio de Janeiro, Rio de Janeiro-RJ CEP:21.945-...

In many applications (e.g. recognition of geophysical and biomedical signals and multiscale analysis of images), it is of interest to analyze and recognize phenomena occuring at different scales. The recently introduced wavelet transforms provide a time-and-scale decomposition of signals that offers the possibility of such analysis. At present, however, there is no corresponding statistical fra...