Stationary exponential time series : further model development and a residual analysis

Abstract

A second order autoregressive process in exponential variables, NEAR(2), is established: the distributional assumptions involved in this model highlight a yery broad four parameter structure which combines five exponential random variables into a sixth exponential random variable. The dependency structure of the NEAR(2) process beyond and including autocorrelations is explored using some new ideas on residual analysis for non-normal processes with autoregressive correlation structure. Other applications of the exponential structure are considered briefly. These include exponential time series with negative correlation and exponential time series with mixed autoregressive-moving average structure. An application to the analysis of a set of wind speed data is included.