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无需固定模型集上界的自回归阶数递归估计AI 解读

SUMMARY In a recent paper, we proved that Rissanen's 'predictive least squares' (PLS) criterion for model selection provides strongly consistent order estimates for autoregressive (AR) processes, i.e. the PLS order estimate p̂(n) based on the first n data points converges almost surely to p 0 as n → ∞ when the data are generated by an AR process of order p 0, and p 0 is known to belong to the finite model set M = {1, 2, ..., K}, K < ∞. In the present paper we strengthen this…

自回归阶数选择中预测最小二乘准则的强一致性AI 解读

This note concerns the problem of order determination for autoregressive models. Rissanen's "Predictive least squares principle" prescribes that one should choose as order estimate $\hat{k}(n)$ at time $n$ the order of the model which has given the least mean square prediction error up to that time. We show that this procedure is strongly consistent, that is, that $\hat{k}(n) \rightarrow p$ a.s. as $n \rightarrow \infty$ when the data are generated by an AR process of order $p$…