Non‐Negative Autoregressive Models

. Consider a stationary non‐negative autoregressive (AR) model given xt=b1xt‐1, +…+bpxt‐p+et, where the et are independent identically distributed non‐negative variables and b1, …, bp are non‐negative parameters, and all the roots of the equation 1 –b1u–…–bpup= 0 are outside the unit circle. The stationary solution of the above AR model is called a stationary non‐negative AR process. Let x1, x2, …xn be an example of a stationary non‐negative AR process. Under very general conditions strongly consistent estimators of the AR parameters b1, b2, …, bp have been studied. In this paper a new procedure is proposed to estimate not only b1, b2, …, bp but also bo which is the essential lower bound of the variable et. We shall show that the new estimators obtained using the new procedure are consistent estimators of bo, b1, …, bp under the weakest condition which guarantees that the stationary non‐negative AR model has a stationary non‐degenerative solution.