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近非平稳 AR(1) 过程的高斯似然估计AI 解读

An asymptotic analysis is presented for estimation in the three-parameter first-order autoregressive model, where the parameters are the mean, autoregressive coefficient and variance of the shocks. The nearly nonstationary asymptotic model is considered wherein the autoregressive coefficient tends to 1 as sample size tends to $\infty$. Three different estimators are considered: the exact Gaussian maximum likelihood estimator, the conditional maximum likelihood or least…

近非平稳自回归时间序列的最大似然型估计AI 解读

The nearly nonstationary first-order autoregression is a sequence of autoregressive processes $y_n(k + 1) = \phi_ny_n(k) + \varepsilon(k + 1), 0 \leq k \leq n$, where the $\varepsilon(k)$'s are iid mean zero shocks and the autoregressive coefficient $\phi_n = 1 - \beta/n$ for some $\beta > 0$, so that $\phi_n \rightarrow 1$ as $n \rightarrow \infty$. We consider a class of maximum likelihood type estimators called $M$ estimators, which are not necessarily robust. The…