Fast cars

This paper develops methods for quickly computing maximum likelihood conditional autoregressions(CARs).By using sparse matrix methods,reorganizing the sum-of-squared errors function to avoid unnecessary calculations,and precomputing a set of determinants,simulations of large CARs become possible. As an illustration of the power of these approaches,a simulation of 250 CARs of 2,905 observations can take fewer than three minutes on a personal computer,despite the necessity of evaluating 100 determinants of 2,905 by 2,905 matrices.The computation of each estimate via examining the profile likelihood sampled at 100 points avoids problems of local optima.Simulating estimates avoids other problems associated with the traditional information matrix approach to inference.