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马尔可夫转换观测驱动模型最大似然估计量的渐近性质AI 解读

A Markov-switching observation-driven model is a stochastic process $((S_t,Y_t))_{t \in \mathbb{Z}}$ where $(S_t)_{t \in \mathbb{Z}}$ is an unobserved Markov chain on a finite set and $(Y_t)_{t \in \mathbb{Z}}$ is an observed stochastic process such that the conditional distribution of $Y_t$ given $(Y_τ)_{τ\leq t-1}$ and $(S_τ)_{τ\leq t}$ depends on $(Y_τ)_{τ\leq t-1}$ and $S_t$. In this paper, we prove consistency and asymptotic normality of the maximum likelihood estimator…

关于条件异方差时间序列拟极大似然估计的随机递推方法的一则注记AI 解读

Bougerol (1993) and Straumann and Mikosch (2006) gave conditions under which there exists a unique stationary and ergodic solution to the stochastic difference equation $Y_t \overset{a.s.}{=} Φ_t (Y_{t-1}), t \in \mathbb{Z}$ where $(Φ_t)_{t \in \mathbb{Z}}$ is a sequence of stationary and ergodic random Lipschitz continuous functions from $(Y,|| \cdot ||)$ to $(Y,|| \cdot ||)$ where $(Y,|| \cdot ||)$ is a complete subspace of a real or complex separable Banach space. In the…