Evidence for Autoregressive Conditional Heteroskedastic errors in growth traits of beef cattle

Abstract. Evidence is presented for "generalized autoregressive conditional heteroskedasticity" processes (GARCH(1,1)), in the residuals of beef cattle growth traits. This process can account for differences in variance at different time points, with the advantage of using a parsimonious parametrization. Data used were 10271 birth weights (BW), 19992 weaning weights (WW) and 9717 weight at 18 months (FW), from five herds registered in the national evaluation of the Brangus breed in Argentina. The residuals calculated from the 2005 genetic evaluation were regressed on Julian dates by least squares. From a second set of residuals out of the linear regression model, Maximum Likelihood estimation via the Fisher scoring algorithm was used to estimate the GARCH(1,1) parameters. Eight out of fifteen one-sided Lagrange multiplier statistics significantly (P < 0.05) rejected the hypothesis of null GARCH(1,1) parameters in the genetic evaluation residuals. Incorporating these effects in genetic evaluation is feasible due to the diagonal covariance matrix induced by the process on each trait, which simplifies building the mixed model equations.