Two-step estimation for time varying ARCH models
Two-step estimation for time varying ARCH models
复制标题
时变 ARCH 模型的两步估计
DOI：
10.1111/jtsa.12522
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发表时间：
2020
影响因子：
0.9
通讯作者：
Yang Lijian
中科院分区：
文献类型：
--
作者：
Zhang Yuanyuan;Liu Rong;Shao Qin;Yang Lijian
提出了一个描述金融收益率序列在长时间内波动性变化的时变自回归条件异方差模型，沿着两步最小二乘和极大似然估计方法.在对波动率尺度的时变趋势进行初步估计后，得到了对潜平稳平稳序列的近似，并利用该近似计算了波动率系数的最小二乘估计（LSE）和极大似然估计（MLE）。在初等和温和的假设下，证明了两步最小二乘估计对未知系数的预言有效性，即两步最小二乘估计与基于不可观测序列的不可行最小二乘估计一样渐近有效.事实上，两步LSE偏离不可行LSE opn−1/2。然而，两步极大似然估计并不具有这样的效率，但是对于两步极大似然估计及其与不可行极大似然估计的偏差，都建立了n/2渐近正态性。模拟研究证实了渐近理论，并将其应用于1950年至2018年的标准普尔500指数日收益率，表明波动率规模随时间发生了显着变化。
A time varying autoregressive conditional heteroskedasticity (ARCH) model is proposed to describe the changing volatility of a financial return series over long time horizon, along with two‐step least squares and maximum likelihood estimation procedures. After preliminary estimation of the time varying trend in volatility scale, approximations to the latent stationary ARCH series are obtained, which are used to compute the least squares estimator (LSE) and maximum likelihood estimator (MLE) of the ARCH coefficients. Under elementary and mild assumptions, oracle efficiency of the two‐step LSE for ARCH coefficients is established, that is, the two‐step LSE is asymptotically as efficient as the infeasible LSE based on the unobserved ARCH series. As a matter of fact, the two‐step LSE deviates from the infeasible LSE by opn−1/2. The two‐step MLE, however, does not enjoy such efficiency, butn1/2asymptotic normality is established for both the two‐step MLE as well as its deviation from the infeasible MLE. Simulation studies corroborate the asymptotic theory, and application to the S&P 500 index daily returns from 1950 to 2018 indicates significant change in volatility scale over time.