When Moving-Average Models Meet High-Frequency Data: Uniform Inference on Volatility
When Moving-Average Models Meet High-Frequency Data: Uniform Inference on Volatility
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DOI：
10.2139/ssrn.3043834
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发表时间：
2017-08
期刊：
影响因子：
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通讯作者：
R. Da;D. Xiu
中科院分区：
文献类型：
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作者：
R. Da;D. Xiu
我们提出了带噪声的高频数据对波动率的一致有效推断。我们假设观察到的交易价格服从连续时间的Ito-半鞅，并被与交易到达相关的离散时间移动平均噪声过程污染。我们通过最大化错误指定的移动平均模型的可能性来估计半鞅的二次方差，该移动平均模型的阶数是基于信息准则选择的。我们的推论在一大类噪声过程上是一致有效的，这些噪声过程的大小和依赖结构随样本大小而变化。我们的实现是调谐自由限制顺序选择，并且在有限样本中产生正估计。最后，我们提供了噪声自协方差的一致估计作为副产品，这在实现一致性方面也起着关键作用。
We propose uniformly valid inference on volatility with noisy high-frequency data. We assume the observed transaction price follows a continuous-time Ito-semimartingale, contaminated by a discrete-time moving-average noise process associated with the arrival of trades. We estimate the quadratic variation of the semimartingale by maximizing the likelihood of a misspecified moving-average model, with its order selected based on the information criteria. Our inference is uniformly valid over a large class of noise processes whose magnitude and dependence structure vary with sample size. Our implementation is tuning free barring order selection, and it yields positive estimates in finite samples. Finally, we provide consistent estimators of noise autocovariances as byproducts, which also play a critical role in achieving uniformity.