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高频数据下的高维回归系数检验AI 解读

This paper presents the first study on high-dimensional regression coefficient tests with high-frequency financial data. These tests allow the number of regressors to be larger than the number of observations within each estimation block and can grow to infinity in asymptotics. In this paper, the sum-type test and max-type test have been proposed, where the former is suitable for the dense alternative (many small betas) and the latter is suitable for the sparse alternative…

异步、含噪与高维高频数据的已实现回归AI 解读

We develop regression for high frequency data. This regression is novel in that it can be for both fixed and increasing dimension. Also, the data may have microstructure noise, and observations (trades, or quotes) can be asynchronous, (i.e., the observations do not need to be synchronized across dimensions). As is customary for high-frequency inference methods, we refer to our method as “realized” regression.

二阶差分估计量的中心极限定理及波动率与强度应用AI 解读

In this paper, we introduce a general method for estimating the quadratic covariation of one or more spot parameter processes associated with continuous time semimartingales, and present a central limit theorem that has this class of estimators as one of its applications. The class of estimators we introduce, that we call Two-Scales Quadratic Covariation (TSQC) estimators, is based on sums of increments of second differences of the observed processes, and the intervals over…

观测渐近方差：强边缘效应与回归方法AI 解读

High frequency financial data has become an essential component of the digital economy, yielding an increasing number of estimators. However, it is hard to reliably assess the uncertainty of such estimators. The Observed Asymptotic Variance (observed AVAR) is a non-parametric estimator for (squared) standard error in high frequency data. The device is related to observed information in likelihood theory, but in this case it is non-parametric and uses the high-frequency data…

桥下的五个巨魔：异步且含噪高频数据的主成分分析AI 解读

We develop a principal component analysis (PCA) for high frequency data. As in Northern fairy tales, there are trolls waiting for the explorer. The first three trolls are market microstructure noise, asynchronous sampling times, and edge effects in estimators. To get around these, a robust estimator of the spot covariance matrix is developed based on the smoothed two-scale realized variance (S-TSRV). The fourth troll is how to pass from estimated time-varying covariance…

双尺度估计的代数性质与S-TSRV：对采样时点稳健的高频估计AI 解读

In this paper, we derive a new algebraic property of two scales estimation in high frequency data, under which the effect of sampling times is canceled to high order. This is a particular robustness property of the two scales construction. In general, irregular, asynchronous, or endogenous times can cause problems in estimators based on equidistant observation of (trade or quote) times.

识别高频数据中非平稳微观结构噪声与时变流动性的无模型方法AI 解读

In this paper, we provide non-parametric statistical tools to test stationarity of microstructure noise in general hidden Itô semimartingales, and discuss how to measure liquidity risk using high-frequency financial data. In particular, we investigate the impact of non-stationary microstructure noise on some volatility estimators, and design three complementary tests by exploiting edge effects, information aggregation of local estimates and high-frequency asymptotic…

内生采样时点下积分二次协变动的估计AI 解读

When estimating high-frequency covariance (quadratic covariation) of two arbitrary assets observed asynchronously, simple assumptions, such as independence, are usually imposed on the relationship between the prices process and the observation times. In this paper, we introduce a general endogenous two-dimensional nonparametric model. Because an observation is generated whenever an auxiliary process called observation time process hits one of the two boundary processes, it…

高频数据的不确定性评估：观测渐近方差AI 解读

The availability of high frequency financial data has generated a series of estimators based on intra-day data, improving the quality of large areas of financial econometrics. However, estimating the standard error of these estimators is often challenging. The root of the problem is that traditionally, standard errors rely on estimating a theoretically derived asymptotic variance, and often this asymptotic variance involves substantially more complex quantities than the…

数据清洗与推断之间：预平均及有效价格的稳健估计AI 解读

Pre-averaging is a popular strategy for mitigating microstructure in high frequency financial data. As the term suggests, transaction or quote data are averaged over short time periods ranging from 30 s to five min, and the resulting averages approximate the efficient price process much better than the raw data. Apart from reducing the size of the microstructure, the methodology also helps synchronise data from different securities. The procedure is robust to short term…

采样时点可能内生时的已实现波动率AI 解读

When estimating integrated volatilities based on high-frequency data, simplifying assumptions are usually imposed on the relationship between the observation times and the price process. In this paper, we establish a central limit theorem for the realized volatility in a general endogenous time setting. We also establish a central limit theorem for the tricity under the hypothesis that there is no endogeneity, based on which we propose a test and document that this…

利用高频数据估计杠杆效应AI 解读

The leverage effect has become an extensively studied phenomenon that describes the (usually) negative relation between stock returns and their volatility. Although this characteristic of stock returns is well acknowledged, most studies of the phenomenon are based on cross-sectional calibration with parametric models. On the statistical side, most previous works are conducted over daily or longer return horizons, and few of them have carefully studied its estimation,…

均衡价格跳跃与市场微观结构噪声AI 解读

Asset prices observed in financial markets combine equilibrium prices and market microstructure noise. In this paper, we study how to tell apart large shifts in equilibrium prices from noise using high frequency data. We propose a new nonparametric test which allows us to asymptotically remove the noise from observable price data and to discover jumps in fundamental asset values. We provide its asymptotic distribution to decide when such jumps occur. In finite samples, our…

已实现波动率及相关估计量的 Edgeworth 展开AI 解读

This paper shows that the asymptotic normal approximation is often insufficiently accurate for volatility estimators based on high frequency data. To remedy this, we derive Edgeworth expansions for such estimators. The expansions are developed in the framework of small-noise asymptotics. The results have application to Cornish-Fisher inversion and help setting intervals more accurately than those relying on normal distribution.

相关微观结构噪声下的超高频波动率估计AI 解读

We analyze the impact of time series dependence in market microstructure noise on the properties of estimators of the integrated volatility of an asset price based on data sampled at frequencies high enough for that noise to be a dominant consideration. We show that combining two time scales for that purpose will work even when the noise exhibits time series dependence, analyze in that context a refinement of this approach is based on multiple time scales, and compare…

离散及随机采样扩散过程的 Hansen–Scheinkman 矩估计量分析AI 解读

We derive closed-form expansions for the asymptotic distribution of Hansen and Scheinkman [1995. Back to the future: generating moment implications for continuous-time Markov processes. Econometrica 63, 767-804] moment estimators for discretely, and possibly randomly, sampled diffusions. This result makes it possible to select optimal moment conditions as well as to assess the efficiency of the resulting parameter estimators relative to likelihood-based estimators, or to an…

随机间隔离散观测下扩散过程估计量的一般理论AI 解读

We provide a general method to analyze the asymptotic properties of a variety of estimators of continuous time diffusion processes when the data are not only discretely sampled in time but the time separating successive observations may possibly be random. We introduce a new operator, the generalized infinitesimal generator, to obtain Taylor expansions of the asymptotic moments of the estimators. As a special case, our results apply to the situation where the data are…

双侧删失数据的自洽估计与极大似然估计算法AI 解读

The paper investigates the structure of the self-consistent estimators (SCE) and the nonparametric maximum likelihood estimator (NPMLE) for doubly censored data. An explicit sufficient and necessary condition for an SCE to be the NPMLE is given. Based on this, algorithms for computing the SCE and the NPMLE are provided. The relation between our algorithms and the EM algorithm is studied.

非线性实验：最优设计与基于似然的推断AI 解读

Nonlinear experiments involve response and regressors that are connected through a nonlinear regression-type structure. Examples of nonlinear models include standard nonlinear regression, logistic regression, probit regression. Poisson regression, gamma regression, inverse Gaussian regression, and so on. The Fisher information associated with a nonlinear experiment is typically a complex nonlinear function of the unknown parameter of interest. As a result, we face an awkward…