ESTIMATION OF THE PARAMETERS INVOLVED IN A 1ST-ORDER AUTOREGRESSIVE PROCESS FOR CONTEMPORARY GROUPS

A methodology was developed for estimating the parameters involved in a first-order autoregressive process; these parameters comprise a vari ance component associated with the random effect, a correlation coeffi cient, rho, and a residual variance. These parameters were estimated u sing REML with an expectation-maximization algorithm. For two single-t rait analyses (milk and fat production being the dependent variable), the example chosen for the analyses was year-month-treated as random a nd following a first-order autoregressive process-within fixed herd. I nitially, estimates failed to converge, possibly because of a time tre nd in the data, which was not accounted for by the model. After the ra ndom effect that follows the first-order autoregressive process was re defined as month within fixed herd-year, the parameters converged, and rho was estimated as .8 for milk and fat yield. Results suggest that the estimation procedures may be useful for situations when a first-or der autoregressive process seems appropriate.