Recursive estimation of mixed autoregressive-moving average order
提出一种递归算法，通过嵌入双变量自回归来高效估计自回归滑动平均模型的阶数(p,q)，并给出渐近性质。
The order, (p, q), of an autoregressive-moving average sequence, y(t), may be estimated by minimizing a criterion, log σ^2+(p+q)logT/T with respect to p and q, where is the maximum likelihood estimate of the variance of the innovations, ε(t). It is suggested that, instead, be estimated from a series of regressions of y(t) on y(t-1),y(t-2),…,y(t-p),ɛ^(t-1),…ɛ^(t-q), where the (t) are obtained by fitting a long autoregression to the data. It is shown how the sequence of regressions may, for p = q, be economically recursively calculated by embedding them in a sequence of bivariate autoregressions. Asymptotic properties of the procedure are established under very general conditions.