HARK the SHARK: Realized Volatility Modeling with Measurement Errors and Nonlinear Dependencies
针对实现方差线性模型忽略测量误差和非线性动态的问题，提出了HAR模型的三种扩展（HARK、SHAR、SHARK），通过结合渐近理论和卡尔曼滤波，在模拟和真实数据上提升了波动率预测效果。
Abstract 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.