We study the problem of estimating higher-order stochastic volatility [SV$\left(p\right)$] models. Due to the difficulty of evaluating the likelihood function, this remains a challenging problem, even in the relatively simple SV$\left(1\right)$ case. We propose simple moment-based winsorized ARMA-type estimators, which are computationally inexpensive and remarkably accurate. The proposed estimators do not require choosing a sampling algorithm, initial parameter values, or an auxiliary model. We show that a Durbin–Levinson-type updating algorithm can be applied to recursively estimate models of increasing order $p$. The asymptotic distribution of the estimators is established. Due to their computational simplicity, the proposed estimators allow one to perform finite-sample Monte Carlo tests. Simulation results show that the proposed estimators have lower bias and mean squared error than all alternative estimators (including Bayes-type estimators). The proposed estimators are applied to S&P 500 daily returns (1928–2016). We find that an SV$\left(3\right)$ model is preferable to an SV(1) model.

我们研究估计高阶随机波动率的问题 [SV$\left(磷\right)$] 楷模。由于评估似然函数的难度，这仍然是一个具有挑战性的问题，即使在相对简单的 SV$\left(1\right)$案件。我们提出了简单的基于矩的 winsorized ARMA 型估计器，其计算成本低且非常准确。建议的估计器不需要选择采样算法、初始参数值或辅助模型。我们表明，Durbin-Levinson 型更新算法可用于递归估计递增阶模型$磷$. 估计量的渐近分布成立。由于它们的计算简单，建议的估计器允许执行有限样本蒙特卡罗测试。仿真结果表明，所提出的估计量比所有替代估计量（包括贝叶斯型估计量）具有更低的偏差和均方误差。建议的估计量适用于标准普尔 500 指数的每日回报（1928-2016 年）。我们发现一个 SV$\left(3\right)$ 模型优于 SV(1) 模型。