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英文文献：Testing for heteroscedasticity in jumpy and noisy high-frequency data: A resampling approach-在跳动和嘈杂的高频数据中检验异方差:重采样方法
英文文献作者：Kim Christensen,Ulrich Hounyo,Mark Podolskij
英文文献摘要：
In this paper, we propose a new way to measure and test the presence of time-varying volatility in a discretely sampled jump-diffusion process that is contaminated by microstructure noise. We use the concept of pre-averaged truncated bipower variation to construct our t-statistic, which diverges in the presence of a heteroscedastic volatility term (and has a standard normal distribution otherwise). The test is inspected in a general Monte Carlo simulation setting, where we note that in finite samples the asymptotic theory is severely distorted by infinite-activity price jumps. To improve inference, we suggest a bootstrap approach to test the null of homoscedasticity. We prove the first-order validity of this procedure, while in simulations the bootstrap leads to almost correctly sized tests. As an illustration, we apply the bootstrapped version of our t-statistic to a large cross-section of equity high-frequency data. We document the importance of jump-robustness, when measuring heteroscedasticity in practice. We also find that a large fraction of variation in intraday volatility is accounted for by seasonality. This suggests that, once we control for jumps and deate asset returns by a non-parametric estimate of the conventional U-shaped diurnality profile, the variance of the rescaled return series is often close to constant within the day.
本文提出了一种测量和测试微结构噪声污染下离散采样跳扩散过程时变挥发性的新方法。我们使用预平均截断双幂变异的概念来构造我们的t统计量，它在异方差波动项存在时发散(否则具有标准正态分布)。该测试在一般蒙特卡洛模拟环境中进行检验，其中我们注意到，在有限的样本中，无穷活度价格跳跃严重扭曲了渐近理论。为了改进推理，我们提出了一种bootstrap方法来检验同方差的零值。我们证明了一阶有效性的过程，而在模拟bootstrap导致几乎正确大小的测试。作为一个例子，我们将t统计数据的bootstrap版本应用到股票高频数据的大截面上。在实际测量异方差时，我们记录了跳变鲁棒性的重要性。我们还发现，日内波动率的很大一部分变化是由季节性引起的。这表明，一旦我们通过传统u形日性剖面的非参数估计来控制跳跃和降低资产回报，重新调整的回报序列的方差通常在一天内接近常数。
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