Consider a stationary autoregressive process given by XI = b,X,-, + . . . + b,X,-, + Y;, where the I; are independent identically distributed positive variables and b,, . . . , b, are non-negative parameters. Let the variables XI,. . . , X, be given. If p = 1 then it is known that b: = min(XJX1-,) is a strongly consistent estimator for b, under very general conditions. In this paper the case p = 2 is analysed in detail. It is proved that rnin(X,/X,-,) + b, almost surely (a.s.) and min(XJX,-,) + b, + b: a.s. as n + to. The convergence is very slow. Denote by b: and b: values of b, and b, respectively which maximize b, + b, under the conditions X, -b,X,-, -b,X,-2 2 0 for t = 3, . . . , n. We prove that b: + b, and b: + b, a.s. Simulations show that by and b:are better than the least-squares estimators of the autoregressive coefficients when the distribution of Y; is exponential.