Estimation of the integrated volatility using noisy high-frequency data with jumps and endogeneity

In this paper, we investigate a new estimator of the integrated volatility of Itô semimartingales in the presence of both market microstructure noise and jumps when sampling times are endogenous. In the first step, our estimation wipes off the effects of the microstructure noise, and in the second step our estimator shrinks the effects of jumps. We provide consistency of the estimator when the jumps have finite variation and infinite variation and establish a central limit theorem for the estimator in a general endogenous time setting when the jumps only have finite variation. Simulation illustrates the performance of the proposed estimator.     

Asymptotic distributions in affiliation networks with an increasing sequence

A central limit theorem for a linear combination of all the maximum likelihood estimators with an increasing dimension for affiliation networks has been established. Simulation studies are provided to illustrate the asymptotic results.     

A note on stable limit theory for the OLSE with non usual rates and the heteroskedasticity robust Wald test

We are occupied with an example concerning the limit theory of the ordinary least squares estimator (OLSE) when the innovation process of the regression has the form of a martingale transform the iid part of which lies in the domain of attraction of an α-stable distribution, the scaling sequence has a potentially diverging truncated α-moment, and the regressor process has a potentially divergent truncated second moment. We obtain matrix rates that reflect the stability parameter as well as the slow variations present in the aforementioned sequences, and stable limits. We also derive asymptotic exactness, consistency, and local asymptotic unbiasedness under appropriate local alternatives for a heteroskedasticity robust Wald test based on subsampling. The results could be useful for inference on the factor loadings in an instance of the APT model.     

The conditional maximum of Poisson random variables

The conditional maxima of independent Poisson random variables are studied. A triangular array of row-wise independent Poisson random variables is considered. If condition is given for the row-wise sums, then the limiting distribution of the row-wise maxima is concentrated onto two points. The result is in accordance with the classical result of Anderson. The case of general power series distributions is also covered. The model studied in Theorems 2.1 and 2.2 is an analogue of the generalized allocation scheme. It can be considered as a non homogeneous generalized scheme of allocations of at most n balls into N boxes. Then the maximal value of the contents of the boxes is studied.     

Optimal Berry–Esseen bound for parameter estimation of SPDE with small noise

We investigate a rate of convergence on asymptotic normality of the maximum likelihood estimator (MLE) for parameter $\theta$ appearing in parabolic SPDEs of the form

$d{u}^{?}(t,x)=(A_0+\theta A_1)u^{?}(t,x)dt+?dW(t,x),$

where $A_0$ and$A_1$ are partial differential operators, $W$ is a cylindrical Brownian motion (CBM) and $?\downarrow 0$. We find an optimal Berry–Esseen bound for central limit theorem (CLT) of the MLE. It is proved by developing techniques based on combining Malliavin calculus and Stein’s method.     

Mildly explosive autoregression with mixing innovations

In this paper, the limit distribution of the least squares estimator for mildly explosive autoregressive models with strong mixing innovations is established, which is shown to be Cauchy as in the iid case. The result is applied to identify the onset and the end of an explosive period of an econometric time series. Simulations and data analysis are also conducted to demonstrate the usefulness of the result.     

Limit Theorems for the Counting Process of Near-Records

Near-records of a sequence, as defined in Balakrishnan et al. (2005 Balakrishnan , N. , Pakes , A. G. , Stepanov , A. ( 2005 ). On the number and sum of near-record observations . Advances in Applied Probability 37 : 765 – 780 .[Crossref], [Web of Science ®] , [Google Scholar]), are observations lying within a fixed distance of the current record. In this article we study the asymptotic behavior of the number of near-records, among the first n observations in a sequence of independent, identically distributed and absolutely continuous random variables. We give conditions for the finiteness of the total number of near-records as well as laws of large numbers for their counting process. For distributions with a finite number of near-records, we carry out a simulation study suggesting that the total number of near-records has a geometric distribution.     

会计盈余信息选拔的不可能定理及其理论深化

在美国等较为成熟的股票市场中,会计盈余信息的主要功能是定价,但是在政府管制较为严格的中国股票市场中,会计盈余信息的首要功能是"选拔".文章对中国证监会和上市公司之间的博弈构建了数学模型,提出了"会计盈余信息选拔的不可能定理":若以下两个条件存在--(1)监管部门设定选拔标准有一个上限,或(2)上市公司通过合法或非法方式虚报盈余的"虚报成本系数"较小,那么单纯依靠会计盈余信息将无法选拔出理想的目标公司.由此得到的可能的理论深化是:度量标准应当与契约形式相配合,如果制度环境本身限制了会计盈余信息作为度量标准的使用,那么改善的要点不应该集中于会计盈余信息本身,而应该在于调整博弈制度的安排.同时也为中国新会计准则执行研究提供了新的理论视角.     

The Realized Laplace Transform of Volatility

We introduce and derive the asymptotic behavior of a new measure constructed from high‐frequency data which we call the realized Laplace transform of volatility. The statistic provides a nonparametric estimate for the empirical Laplace transform function of the latent stochastic volatility process over a given interval of time and is robust to the presence of jumps in the price process. With a long span of data, that is, under joint long‐span and infill asymptotics, the statistic can be used to construct a nonparametric estimate of the volatility Laplace transform as well as of the integrated joint Laplace transform of volatility over different points of time. We derive feasible functional limit theorems for our statistic both under fixed‐span and infill asymptotics as well as under joint long‐span and infill asymptotics which allow us to quantify the precision in estimation under both sampling schemes.