Despite their effectiveness, linear models for realized variance neglect measurement errors on integrated variance and exhibit several forms of misspecification due to the inherent nonlinear dynamics of volatility. We propose new extensions of the popular approximate long-memory heterogeneous autoregressive (HAR) model apt to disentangle these effects and quantify their separate impact on volatility forecasts. By combining the asymptotic theory of the realized variance estimator with the Kalman filter and by introducing time-varying HAR parameters, we build new models that account for: (i) measurement errors (HARK), (ii) nonlinear dependencies (SHAR) and (iii) both measurement errors and nonlinearities (SHARK). The proposed models are simply estimated through standard maximum likelihood methods and are shown, both on simulated and real data, to provide better out-of-sample forecasts compared to standard HAR specifications and other competing approaches.

中文翻译：

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助力鲨：具有测量误差和非线性相关性的已实现波动率建模*

尽管具有有效性，但用于实现已实现方差的线性模型却忽略了积分方差的测量误差，并且由于固有的波动性非线性动力学而表现出多种形式的错误指定。我们提出了流行的近似长记忆异质自回归（HAR）模型的新扩展，这些模型易于消除这些影响并量化它们对波动率预测的单独影响。通过将实现的方差估计量的渐近理论与卡尔曼滤波器相结合，并引入时变的HAR参数，我们建立了新模型来说明以下问题：（i）测量误差（HARK），（ii）非线性相关性（SHAR）和（ iii）测量误差和非线性（SHARK）。可以通过标准的最大似然方法简单地估算提出的模型，并在模拟数据和实际数据上进行显示，