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非平稳时间序列中稳定分布与 Hurst 指数的自适应移动矩估计AI 解读

Nonstationarity of real-life time series requires model adaptation. In classical approaches like ARMA-ARCH there is assumed some arbitrarily chosen dependence type. To avoid their bias, we will focus on novel more agnostic approach: moving estimator, which estimates parameters separately for every time $t$: optimizing $F_t=\sum_{τ<t} (1-η)^{t-τ} \ln(ρ_θ(x_τ))$ local log-likelihood with exponentially weakening weights of the old values. In practice such moving estimates can…

面向非平稳时间序列的自适应 Student t 分布与移动矩估计AI 解读

The real life time series are usually nonstationary, bringing a difficult question of model adaptation. Classical approaches like ARMA-ARCH assume arbitrary type of dependence. To avoid their bias, we will focus on recently proposed agnostic philosophy of moving estimator: in time $t$ finding parameters optimizing e.g. $F_t=\sum_{τ<t} (1-η)^{t-τ} \ln(ρ_θ(x_τ))$ moving log-likelihood, evolving in time. It allows for example to estimate parameters using inexpensive exponential…