Extremely Fast Maximum Likelihood Estimation of High‐Order Autoregressive Models
提出一种基于坐标下降的极快算法，用于高阶自回归模型的精确极大似然估计，比现有算法快数个数量级，并扩展到多时间序列和带自回归残差的回归。
ABSTRACT We consider the problem of exact maximum likelihood estimation of potentially high‐order () autoregressive models. We propose an extremely fast coordinate‐wise algorithm for fitting autoregressive models. This fast algorithm exploits several properties of the negative log‐likelihood when parameterised in terms of partial autocorrelations. We consider extensions to learning a single autoregressive model from multiple time series and to the more general case of regressions with autoregressive residuals. An implementation of the coordinate‐wise descent algorithm is shown to be the orders of magnitude faster than competing algorithms and appears to be the fastest known algorithm for maximum likelihood estimation of autoregressive models.